I wouldn't level up using Fates as suggested, follow the storyline, more gil, equipment rewards, and you will learn different mob mechanics, also a little lore doesn't hurt.

Dungeons are good for exp and keep you thinking as part of a team.

Most decent equipment will be rewarded to you, that is not as much a concern as learning your rotations to get the maximum output and efficiency imo

Join a FC - Good advice can be found by reading what others are writing in the chatbox.