There has been some good answers already but two things I wanted to note is that your first powerful card given early on is Ifrit and you should ALWAYS make sure to speak with the NPC on the second floor near the elevator when starting the game to receive a starter set of cards. You receive the Ifrit card when you beat Ifrit in the Fire Cavern.Guys, I have a legitimate question before this game comes out:
So, I've never really played Triple Triad. My first couple of playthroughs I pretty much ignored it entirely bc I was very young and it was too confusing, and on my last play through, I think I played my first card game like halfway through Disc 1 but literally every single card game I'd play the NPC's would have way better cards than me. If I want to use TT on a regular basis to make myself more powerful, should I pretty much start playing it IMMEDIATELY on my next play through? Any tips/tricks?
Once that is all done you can start challenging NPCs with lower level cards and improve on your current deck. One such NPC is the kid running around garden who has the MiniMog card. The good thing is that there is a save point right near where he runs through so you can always reload if you happen to lose Ifrit and don't want to try getting the card back. Once you have improved on your current deck, you can challenge Zells mom to get his card. When you finally have that card you can try and get Seifer from Cid and Quistis from the Trepies all of which is available early on before leaving for Timber.