Congrats on getting the GameCube:
The GameCube is the only system that plays all of the Resident Evil games (RE0, RE, RE2, RE3, RECVX, RE4).
The GameCube also plays every single Legend of Zelda game ever made. Either through Zelda Collector's Edition or the GameBoy Player.
If you got the GameCube for Zelda Twilight Princess, you may enjoy Star Fox Adventures and definitely Wind Waker. Do not let the cel-shaded graphics make you not buy the game, you will not regret this purchase.
Check out Eternal Darkness and Metal Gear Solid: The Twin Snakes, these games are tons of fun.
Metroid Prime 1 and 2 are also great FPS/ Adventure games.
Also, the best version of Soul Calibur II is on GameCube
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