[The Artist Formerly Known as Hawk]

Going on what Evil just said, I concur with using everyone in every battle. Even if all you do is switch characters in and out and have them guard for a turn they will still get AP, and it keeps everyone levelled up at the same rate. If you don't do this, then some characters, such as Kimahri, can end up severely lagging behind.

Further points on characters and how to level them;

To start with, every character will be on their own section of the sphere grid, and it's a mostly straight run through their own section, but eventualy you'll reach the end and will need to branch off into other areas. Kimahri will be the first to finish, and I like to send him off down Rikkus path first. Auron and Tidus are basically the opposites of each other, so once each has finished his own sections they should really swap places, to aquire all the speed/strength that the other has. Wakka I like to send down Aurons section too, for the extra strength buff. The mages Yuna and Lulu should also swap sides, so they both gain black and white magic and increased magic power. Finally I send Rikku down Lulus path, for the black magics, because she has some seriously untapped magic power, at one point my Rikku was casting more powerful spells than Lulu.

One point I don't agree with Evilness on; Blitzball. I honestly don't get all the hate for it, it seems I'm the only person in the world who liked Blitzball. If it turns out you do wanna play some I can give you tips on team setup and things. Just make sure you learn the Jecht Shot while on the boat after Kilika. Save the game right after the island so if you screw up you can do it again, even if you don't plan on playing Blitz all that much, because Blitz is at the very least good for one thing; Attack Reels. It's an overdrive for Wakka that you have to win, and it's one of the most powerful attacks in the game. Make sure you get it, you won't be dissapointed.

Oh and right after you leave Besaid vilage, head back in and find the dog. Trust me, you'll love what you find.