Don't worry if you don't have the best equipment all the time, it's perfectly okay to go through multiplie dungeons or sections of the story using the same gear. Random armour and weapons will pop out of chests, enemies and come to you as you finish hunts, so don't stress it if Vaan doesn't have a Dragon Shield like all the others or whatever.

Next piece of advice kind of ties into the previous one, but gil is sparse in this game, so don't be throwing your cash around. Invest in skills and magic on the licence board AS YOU NEED THEM. I didn't learn Vox or Stona until the END of the game. I toughed it out with items until Esuna came available.

Learn Quickenings fast. Any extra LP early in the game, I find, is best used to go to the extremities of the board to get three Quickenings for everyone as fast as possible, regardless of whatever licenses you pick up along the way. Aside from having the ultimate trump cards of Quickenings to take out hard bosses/hunts, you'll also benefit from triple MP.

Techniks: Steal, Libra, Charge. Disregard the rest. Techniks are BEYOND useless in this game. Preach for Numerology or Horology all you want, I think it's not worth the effort or the LP. On that note...

Steal often. Pick up Thief's Cuffs as early as you can (Mt. Bur-Omisace, I believe) and steal like nuts. You're pretty much doubling your loot, and therefore doubling your gil if you make a habit of stealing a lot.