I suggest you sign Kyou, who's standing on the bridge leading to Djose Temple, and Tatts, who's somewhere in Kilika. Also, when good players from other teams go out of contract, be sure to sign them up.

Be sure to learn Tidus' Jecht Shot on the boat to Kilika. Walk up to the blitzball on deck to attempt it.

I'm not a blitzball expert, but that advice should help you.