It all depends on your stats but the most important would be ones that open transportation methods and early xp.
From a level 3 I would do
1. Waterfall Quest (30 something attack and strength)
2. Fight Arena (Free attack xp whilst your near there anyway - short quest)
3. Tree Gnome Village (Spirit Trees)
4. Plague City (Ardy Teleport)
5. Tourist Trap (use the reward on agility to skip early tedious levels and give you the requirement for Grand Tree)
6. The Grand Tree
7. Lost City (Pre requisite for Fairy Rings)
8. Fairytale Part 1 (Pre requisite for Fairy Rings)
9. Fairytale Part 2 (upto unlocking fairy rings, stats not needed)
10. Work towards finishing RFD for Gloves (Long quest, high requirements, you will finish all other useful quests MM, DT etc on the grind here)
Don't train your early levels Quest them, it is usually faster xp and your going to have to do the quest at some point anyway, may aswell get it out of the way and skip the tedious part of training at the same time.
E.g. Tourist Trap you need 20 Smithing, complete The Knights Sword
Look here for all the quests xp rewards to help you decide what quests to complete
Quests/Experience rewards