The VG Resource

I really just want to rip from Wii games, but I say Gamecube since they use (mostly) the same hardware

Hi! As a starting point, use Dolphin and its file viewer. If you don't know how to do this, you right click the game, click Properties, and click the right arrow until you see Filesystem. Go into that tab and you can see the files stored in the game.

Any game you're looking to rip from specifically? Games have different file types.
Some more common ones to look out for are .bmd for GameCube models (Mario Sunshine, MK Double Dash, Pikmin 2, etc.) and .brres for Wii archives (a LOT of games)