Game: FFX. It's just the best game ever as far as I'm concerned. Best battle system and character progression system of any game I've ever played! Plus the best minigame ever in Blitzball too, too bad the AI sucks at it which makes it far too easy to win. Still a great minigame despite that though!
Character: Sephiroth. A bit of a toughy to choose a favourite character so I'll just go with one of the most memorable (and badass) villains that has ever appeared in a game!
I probably have just as much time invested in Blitzball as I do the rest of the game itself. I ate that minigame up as a teenager.
What I always really wanted was a Blitzball spinoff game. That with a load more strategies, teams, competitions, multiplayer versus matches etc would have been awesome!