Good choice. Some seem to disagree, but IMO the GameCube is one of the finest consoles ever made.
Some recommendations:
-Resident Evil 4 (!!)
-The Legend of Zelda: Twilight Princess
-The Legend of Zelda: The Wind Waker (and there's also a limited edition which comes with Ocarina of Time Master Quest, definitely worth it)
-Resident Evil REmake
-Eternal Darkness
-F-Zero GX
-Starfox Adventures
-Timesplitters: Future Perfect
-Tales of Symphonia
-Super Mario Sunshine
-Super Smash Bros. Melee
-Paper Mario: The Thousand Year Door
I drink your milkshake.