You start off by challenging that boy who runs around Balamb Garden, he has the MiniMog card, with Ifrit and Mini you can get the Quistis card from one of the Treppe groupies, then with her card, you go and challenge Cid (after the SeeD exam) for the Seifer card, and finally the Diabolos card from the magical lamp makes you practically unbeatable.
The gatekeeper has a whole range of level 5 cards such as the Abyss Worm (1 = 1 Windmill = 20 Tornado with T Mag-RF) and there are troutloads of other amazing cards that can be modded/refined into powerful magic.