-What quests do I need to do?
I'd make unlocking Prifddinas your (long term?) goal for now. There are enough skill and quest requirements to keep you busy for a while. Also, Desert Treasure, and Smoking Kills as you'll want the double slayer points if you're going to be doing combat.
-What area tasks are important to finish quickly?
Not quite sure about this one. The ardougne cloak (3) is useful for farm runs and general thieving, the seers hard/elite tasks unlock the (Elite) Enhanced Excalibur, which is a nice non-degradable offhand weapon (t70 damage and t72 accuracy if I remember correctly, possibly the other way around) with a decent healing ability.
-It seems like everyone is quiet and already level 130+, should I just find another game?
A lot of people are basically just focused on themselves and grinding now, so unless you find a clan or something there will be a lot less "community spirit" than you remember. I'd give this a shot and if you don't like it after a month or two, maybe it's just not the game for you.
As far as catching up to peoples combat levels, combat training is *very* fast now, so it shouldn't take too long to reach 130+. I'd do most of it through slayer or dung for now and if you get bored of that, once you hit 70 attack and defence you can afk hellhounds in guthans for like 300k exp/h.