Boot/Play: Insert GC disc → Wii Menu → "GameCube" channel → Play. Works with zero memory cards inserted.
Save Progress: GameCube games only save to GameCube Memory Cards in Slot A or B (top flap). Wii Internal Flash / SD Card / USB cannot be used for GC saves.
Wii Saves: Wii games save to Wii Internal / SD. Separate partition.
Memory Card Options
Official Nintendo (59 block / 251 block / 1019 block): Reliable, expensive used.
Third-Party (Mad Catz, Nyko, generic 128MB/256MB/512MB/1GB): Cheap, mostly work. Some corrupt on specific games (Animal Crossing, Pokémon).
Buy a 251-block (official) or 128MB+ (3rd party) card. 59-block fills fast (8 blocks per Mario Kart ghost, 19 for Zelda). Keep one card per "era" (GC games only) to avoid corruption.