Quickest way from 40 - 60 attack (not botting)

I need the fastest way to get from 40 - 60 attack. I have 40 strength and 45 defence. Open to all suggestions.

 

Strength level?
Edit: Sorry, didn't see, for f2p, I'd do something in the first floor of the security stronghold, or maybe barbarians. For p2p, rock crabs

 

Rock crabs or experiments, that is how I would do it.

 

It's in the first post.

 

p2p experiments and rock crabs not sure on f2p sorry

 

From Level 31 to 45
1. Kill Hill giants in Edgeville Dungeon or the Wilderness.

A Hill giant
Main article: Hill giant
Combat level: 28
Advantages:

Hill giants always drop big bones, for either selling (they sell for a high amount of coins at the Grand Exchange, although sometimes can take some to shift if selling for the highest price) or training prayer.
They also drop limpwurt roots for either selling or making strength potions.
If a player is training melee and has at least 20 fishing (with feathers) and a hatchet and tinderbox, this method can be very successful as a player can be training attack, defence, strength, fishing, woodcutting, firemaking, prayer, and cooking simultaneously. Only in Edgeville Dungeon, a Brass key is needed. (A Brass key can be found in the Edgeville Dungeon closer to the zombies, or bought from the Grand Exchange)
This is also a great way to obtain money, as the Big bones sell for 650 each at the Grand Exchange, which is nearby(Edgeville Dungeon only).
Disadvantages:
Rangers will hide behind a rock and range Hill giants, making it difficult for you to acquire a kill.
For players with combat levels in the 30s, Hill giants may be a bit harder to kill. Bring plenty of food and best equipment you can use.
This place may get unbelievably crowded, with multiple people competing for each giant. Being a quick clicker with fast reflexes will help a great deal, if you have a touchpad then this may not be the place for you. It is best to log in to an un-crowded world.
Tips:
Memorise a hill giant respawn point and you may get a kill most of the time. (EXTREMELY useful, as most do not use this, will give you a huge advantage knowing where to click when the others do not)
It may be hard to get a kill, so be patient. Try to pay attention to other people's battles so you know when the next hill giant will appear (e.g. If Player A defeats giant at 1:32, and Player B defeats giant at 1:40, go to the spawn point of Player A for a quicker spawn)
Bring an air staff and get Wind rush ready, and when a monster respawns click on the monster. This way rangers won't have advantage over you.
2. Kill Zombies in the 2nd level of the Stronghold of Security.

A Zombie
Main article: Zombie
Combat level: 30
Advantages:

Zombies are aggressive, this makes you training afkable .
The place isn't as crowded as Hill Giants. The ratio from person to monster is 1:2 or 1:3, which is low unlike the ratio at Hill Giants, which is 2:1 or 1:1.
They drop steel arrows, you can sell them for good profit.
Disadvantages:
You need to get past the 1st level of the Stronghold of Security.
Zombies are aggressive only for 5–10 minutes, then you have to re-enter the level.
The drops are not so good.
They have a maximum hit of 40.
3. Kill Hobgoblins found in many places, such as Edgeville Dungeon, Asgarnian Ice Dungeon, or in the Hobgoblin Peninsula outside the Crafting Guild.

A Hobgoblin
Main article: Hobgoblin
Combat level: 28, 42
Advantages:

Drops limpwurt roots, along with other good drops.
They are aggressive.
Asgarnian Ice Dungeon is not crowded, and range attackers cannot reach all the hobgoblins at peninsula, unless they use longbow or come close-up.
They are found in groups of close proximity.
Disadvantages:
They hit hard and accurately.
They have high defence.
4. Kill Zombies or Skeletons in the Varrock sewers or Edgeville Dungeon.

A Skeleton
Main articles: Zombie and Skeleton
Combat levels: 13, 18, 24 (Zombies) and 21, 22, 25, 45 (Skeletons)
Advantages:

They have a decent amount of life points for their level.
Skeletons have weak attack.
Disadvantages:
Their drops are terrible.
This place is better for rangers, causing crowds.
Level 25 skeletons, only ones without rivals, are very deadly.
5. Kill Zombies in the Graveyard of Shadows.
Main article: Zombie

The Graveyard of Shadows
Combat levels: 18, 24
Advantages:

Low level with lots of life points.
Close to Clan Wars, so you can go into the safe free-for-all and get killed, regenerating your health, run energy, and prayer.
Disadvantages:
Level 18s only drop bones, and level 24s drop only bones and low amounts of coins, or air, mind and cosmic runes only if you are very lucky.
Multi-combat area, so many zombies can pile you at once, or someone can steal your kill.
Revenants can attack such as revenant vampire and goblins.
This place is in the Wilderness, so it might be a risky adventure for lower level players.
6. Kill Barbarians in the Gunnarsgrunn Longhall.

Gunnarsgrunn Longhall
Main article: Barbarian
Combat levels: 15, 17
Advantages:

They give very good and fast XP each kill.
There are Cooked meat respawns on the tables for restoring life points, also dropped by barbarians.
Disadvantages:
Can get very crowded.
It is a multi-way combat area so other players can take your kill.
Tips:
In a crowded world such as World 1, there are usually players giving away free food by the fishing area, east of the village.
7. Kill Guards at the entrances of Varrock and numerous locations in Falador.

A guard. Note that guards in Varrock wear yellow and white armour.
Main article: Guard
Combat levels: 19-22
Advantages:

They have low Defence, making it easy to hit them.
People tend to train in the palace, so it is not very crowded.
There is a bank nearby, so you can bank any drops or get food easily.
Not many people train here as their drops are not worthwhile.
Disadvantages:
On top of the wall, where it is least crowded, there are only two Guards.
If it gets crowded, it is nearly impossible to get a fight.
8. Kill King scorpions on Crandor or in the Falador mining dungeon.

A King scorpion
Main article: King scorpion
Combat level: 32
Advantages :

They have low defence, making them easy to hit.
It is not very crowded as people come to Karamja/Crandor to fight Lesser Demons or fish.
They can easily be killed, giving you fast xp.
Aggressive until level 65.
They have weak attacks.
Fast respawn.
Disadvantages:
No drops. Note: some players might find this as an advantage because it means less bank trip and more xp/hour.
The way to them is hard, as you have to run trough the Karamja/Crandor Volcano.
9. Kill Al Kharid warriors in the Al Kharid Palace.

An Al Kharid warrior
Main article: Al Kharid warrior
Combat level: 9
Advantages:

Warriors can be killed within seconds at this level.
The Warriors have a low defence, making it easy to hit the player's max hit often.
Warriors do low damage.
Lumbridge is close by, so on death it does not take long to return.
Works well with pures.
Cabbage spawn in western room for some healing.
Disadvantages:
It's often very crowded.
If you attack a warrior, the ones near you will also attack you.(this may actually work to your advantage if your defence is relatively high as it would allow you to attract many warriors at once, which would allow for lazier training).
Tips:
If crowded, the player could hop onto a low-populated PvP World where there's few people or none at all.
10. Kill Scorpions at the north Al Kharid mining spot.

A Scorpion
Main article: Scorpion
Combat level: 14
Advantages:

Max hit is only 20.
Less crowded.
High lifepoints and low Defence.
It is not a multi-combat area, so no one can still take your kill.
You help low-levelled miners.
Disadvantages:
They hit constantly, therefore low level players need food.
They do not drop anything (for f2p players). Note: some players might find this as an advantage because it means less bank trip and more xp/hour.
They are a little spread out, reducing the kills per hour.
11. Kill Jail guards at Draynor village.

Some Jail guards
Main article: Jail guard
Combat level: 26
Advantages:

They are usually not crowded.
You can hit often because their armour is leatherbody and they have low Defence.
Disadvantages:
They only drop bones.
They are accurate, so food may be needed.
Tips:
It's multi-combat, so if you are weak, you can just ask another stronger player to help.

From Level 46 to 55
Make sure to bring food and put auto-retaliate on so you will automatically attack the monsters.
1. Kill Moss giants in Crandor, in the Wilderness or in the Varrock sewers.

A Moss giant
Main article: Moss giant
Combat levels: 42, 48
Advantages:

Moss Giants drop big bones for Prayer or selling.
There are several chaos rune spawns near the Wilderness Moss Giants.
The Wilderness spawns are usually deserted.
Their attack rate is fairly slow.
600 life points per giant means good experience.
Disadvantages:
Must have started Dragon Slayer to access Crandor (you do not have to complete the quest, just sail to Crandor and do not kill the dragon). This means pures can train here without gaining unwanted defence xp.
Crandor can get crowded at peak times, Varrock sewers often crowded by high-levels (casual kill and loot stealing).
In the Wilderness, revenants can kill you easily if you are not paying attention (they freeze, teleblock and deal massive damage from all three sides of the Combat Triangle).
The ones in Varrock sewers are in a multiway combat area.
2. Kill Black Knights in or near the Black Knights' Fortress or at the Wilderness Wall north of Varrock.

A Black Knight
Main article: Black knight
Combat level: 33
Advantages:

Inside the fortress is a very high number of knights. This area is generally not overly crowded.
They are very good experience.
They have decent drops.
If you have 31+ Prayer, you can recharge your prayer points at the nearby Monastery. You can also ask the monks to heal you for free.
Alternatively, inside the fortress is a chaos altar, so if you have Protect from Melee you can avoid having to go to a bank for food by using Protect from Melee.
Disadvantages:
You can get damaged quite often, and they have high defence.
To go inside the fortress requires completion of Black Knights' Fortress and a bronze medium helmet as well as an iron chainbody.
The nearest bank is in Edgeville, a bit of a walk away.
Tips:
Unlike many training points, scimitars may not do well here because the knights' armour has a high slash defence. Using a crushing
weapon - battleaxe, mace, warhammer or two-handed sword - is recommended as plate armour is weak to crush.
3. Kill White Knights in the White Knights' Castle.

A White Knight
Main article: White knight
Combat levels: 36, 38, 39, 42
Advantages:

They are close to a bank.
The swords wielded by the knights have a slow attack rate.
Crush weapons do well against their armour.
There is a place for training range on the top floor.
Disadvantages:
All of Falador is a multi-combat area, and a decent amount of people train here so you will have to world-hop every so often when it gets crowded.
White Knights hit hard for their level.
Quicker weapons such as daggers and shortswords lack the punch needed to effectively penetrate the knights' defence. A heavier weapon, like a longsword or battleaxe, is definitely recommended.
Tips:
The upper level of the White Knight's Castle is usually not crowded; going there is a good idea.
The upper levels also have more knights than the courtyard.
The lowest level has a chicken that respawns frequently. There is also a cooking range that is fairly close to the chicken.
Using the altar in the Castle, you can use prayers (increase attack, strength, etc.) thus giving you an advantage constantly if you recharge.
4. Kill Deadly red spiders in the Karamja-Crandor dungeon or Varrock Sewers.

A Deadly red spider
Main article: Deadly red spider
Combat level: 34
Advantages:

The Deadly red spiders hit low.
High LP and low defence makes them very good experience source for this levels.
Red spiders' eggs respawn near the spiders.
Aggressive even against high levels.
Disadvantages:
Nearby lesser demons will attack anyone who comes too close, they hit high and often.
Red spiders have no drops for non-members.
There is no bank close by, so you need to conserve your inventory between food, fishing and firemaking gear and spider eggs.
Tips:
Using the Cabbage teleport on the Explorer's Ring 3 will allow you quick access to the Draynor bank. Then you can get 30 gp and rush back to Port Sarim and sail back to Karamja.
If you take food: every time you eat, pick up Red spiders' eggs. This makes up for the cost of food.
You can fish and cook food on Karamja, then use it to train.
5. Kill Flesh crawlers in the 2nd level of the Stronghold of Security.

A Flesh crawler
Main article: Flesh crawler
Combat levels: 25, 38, 41
Advantages:

They have high life points.
They have some decent drops such as uncut gems.
For the most part, they are an aggressive monster.
Very hard to get killed unless you are away from your keyboard for a long time because they can only hit a max of 16.
There's an areas with no zombies
Not in a multi-combat area so they cannot gang up on you.
Disadvantages:
They tend to hit continuously especially on the pures, so you need to pay attention.
Somewhat high defence.
6. Kill Hobgoblins in Edgeville dungeon, Hobgoblin Peninsula, or Ice Caves South of Port Sarim.

A Hobgoblin
Main article: Hobgoblin
Combat levels: 28, 42
Advantages:

They have high life points.
They drop limpwurt roots very often which can be sold at good price.
They are relatively easy to kill at this level.
The Ice Caves are generally uncrowded.
There is a bank nearby if using Edgeville dungeon.
Disadvantages:
They have a high defence level and somewhat accurate.
Level 42 Hobgoblins can hit up to 50 life points.

From Level 56 to 75
1. Kill Catablepons or Giant spiders found in level 3 of the Stronghold of Security.

A Catablepon
Main articles: Catablepon and Giant spider
Combat levels: 50 (Giant spiders) and 49, 64, 68 (Catablepons)
Advantages:

Catablepons drop a piece of the skull sceptre. (Top of Sceptre)
High LP.
Catablepons are usually not crowded.
There are many of them, and they'll attack you regardless of your combat level.
Disadvantages:
Catablepons can drain your strength by up to 10%, which makes it ineffective for warriors.
Giant spiders are often crowded.
They can damage fairly often to Rangers and Mages.
The Giant spiders have no drops.
You need time to find a specific area where only one kind of monsters is available.
Catablepons have very high defence, possibly causing players below level 50 Combat unable to defeat them.
2. Kill Ice warriors or Ice giants in the Ice Caves south of Port Sarim or Ice Plateau in Level 48 Wilderness.

An Ice warrior

An Ice giant
Main articles: Ice warrior and Ice giant
Combat levels: 57 (Ice warrior) and 53 (Ice giant)
Advantages:

These areas are not very crowded.
They respawn quickly.
They have decent drops, with lots of runes such as nature, chaos, death, law and cosmic.
They are aggressive and will attack you.
They drop jugs of wine and bananas which can be used for healing.
Disadvantages:
You have to navigate through rough and dangerous terrain for resupply.
They can hit frequent 60s and 70s.
If only fighting Ice Giants, the Ice warriors can cause a disturbance. After 12–60 minutes, they will stop attacking you.
If training in the Wilderness, be extremely wary of Revenants.
Tips for Wilderness training:
Do not bring anything you are not ready to replace if lost.
Swordfish is a good food to have along.
Always save some food for the trip back.
While training, try to keep over half of your life points intact.
It is suggested to bring a small clan of 4-6 people including you to decrease the possibility of death and item-loss since your friends can repair or even bless your gravestone.
3. Kill Cockroach workers in the Stronghold of Player Safety

A Cockroach worker
Main article: Cockroach worker
Combat level: 56
Advantages:

There are many scattered around on different levels of the area.
Close to the rope that leads to Edgeville (top floor), so if close to death a quick getaway is possible.
This area is nearly always uncrowded.
As with all cockroaches, they have very good drops for their level.
They are not aggressive
Disadvantages:
They hit frequent 50s and 60s.
Watch out for kill-stealers.
They have a good defence.
They don't drop bones, so do not kill them if you plan to advance your prayer level.
4. Kill Zombies or Giant rats found in level 2 of the Stronghold of Security.

A Zombie
Main articles: Zombie and Giant rat
Combat levels: 30, 40, 44, 53 (Zombies) and 26 (Giant rats)
Advantages:

They have low attack.
Good LP.
They have low Defence.
They drop steel arrows, that can be sold at the Grand Exchange for 45 each, you can also choose to save them to train Ranged.
Disadvantages:
Unless you go on one of the worlds with lower amount of people, it is very crowded.
Their damage range is 40-70.
Flesh Crawlers might get in your way, as they are aggressive to ALL LEVELS.

 

I've figured out the best way for me at the moment: Questing. I've got 50 attack now and I've only done about 4 quests. I'm having a friend do Monkey Madness for me tomorrow.

Thank you guys for your suggestions.