I second MistakeNot's suggestion. Focus on main quests (MSQ) at 50 until you get to Ishgard. It's a long slog through the lv 50 MSQ, but you need to do it to unlock he lv 51+ content. The main quest will gear you up through quest rewards and forcing you into dungeons/trials that give poetics tomes you can use to buy gear.

Of course, don't burn out. MSQ can be tiring and it's very long. You can do hunts for allied seals (buys some nice 110 accessories). You do PotD and secure a padjila (ilvl 235) or even kinna (ilvl 255) weapon. You can work on crafter and gatherer classes. You can work up grand company ranks and build a squad to send on missions. You can run some extra dungeons for fun and end up with more poetics tomes than you know what to do with. I did all that and had fun with it.

Oh, if you do end up nearly capping on poetics... buy some unidentified craft materials (300 each). They are used (10 each I think) for the anima weapon at 60 in the first stage. That stage can be skipped with if you did the lv 50 relic weapon entirely (I think). There is no reason to do that lv 50 version though. It will be much quicker and easier to wait to 60 for anima chain. Just make sure you buy something useful with poetics so you don't hit 2k cap. I'm still hazy on the whole relic/anima weapon thing, since I haven't done it yet. Maybe a more experienced player can chime in.