Here's my quickstart tips as an actual, card-carrying idiot:

-Your new abilities are gained from quests from your Job trainer with a chain starting at lvl 50
-That last aether current you need is probably for doing the zone dungeon in the MSQ
-Except that one north of you in Sea of Clouds. You can't get that one yet, try again later after more questing
-Visiting the stables in Ishgard will let you teach your companion Chocobo to fly
-Hunt logs start at 53
-Outside of the ones that get the entire zone cheering, FATEs aren't too worth doing at the moment
-If you don't have your CE items try clearing your inbox
-Moogles