I, too, had a much easier and more fun experience on my second playthrough... though I can't really add to what others have already said, in terms of handy hints.

Except to say that a second game is the perfect opportunity to go for the Zodiac Spear, which kicks many bottoms in rapid succession. There's some level-grinding, boss-fighting and run-for-your-life-ing involved in getting it, but it's well worth it for a weapon that turns one character into a nigh-unstoppable powerhouse while their level is still in the low 20s.

:edit:

Oh yeah... what Demon Dude said about guns: often, it's true. In my current game, I'm keeping Balthier's weapon licenses almost dedicated to gunnery, and it's helpful. The attack number may be low, but guns ignore the enemy's defence stat, so more often than not they'll have an advantage. Especially if you've got a range of elemental and status ammo.

Don't hesitate to use Elixirs whenever necessary. I always tend to hoard mine throughout the game, because of their rarity and power, but that just means I end up with way too many at the final fights.

Given the choice between gaining a few levels and gaining some better armour, go for the armour. Keeping your team's gear up to date is a must, unless you really like resurrecting on every other turn.