TimeSplitters 2 and TimeSplitters Future Perfect are both very good FPSs for the GameCube. The former is much more fast paced and arcadey than the sequel, but the latter has a decent single-player mode behind it, plus some bigger levels, better weapons and mapmaker, and more monkeys.
Animal Crossing is alright, if you like pulling weeds, doing chores, and being in debt to a raccoon. You're probably better off getting one of the sequels for the DS or Wii to be honest, since they seem to offer much more. Plus, it takes a full memory card just to make a save for Animal Crossing.
I also recommend picking up Viewtiful Joe. It's just a blast to play, really. It does get difficult towards the end, but not impossible.
The Metroid Prime games are definitely good. They may not play like other FPSs, but that's something that I liked about them. I only played the second, Echoes, and never got the chance to beat it, but still, they're great nonetheless. Plus, Samus Aran kicks a ton of ass.
Speaking of shooters made by Nintendo, there's also the obscure Geist. It played like most FPSs do and had a weird story that I swear tries to mimic the FEAR games at times, but it was still decent. The main kicker to Geist though was the ability to become a ghost, phase through objects, and possess enemies or the environment and use them to your advantage. Guys with a machine gun standing behind his buddies providing support? Try possessing him and turn him against his former comrades. Even cooler, possessing is possible both in single player and in the multi-player, which you can play with either friends or bots.
Aside from the Metroid Prime games, these should all be rather affordable. Good luck finding them.