hello,
You do not necessarily need a memory card. The Wii itself has 512mb on-board storage. The SD card slot allows expansion cards up to 2gb. As for the gamecube memory card slot, I have no idea....
All gamecube homebrew requires the use of a gamecube controller (I believe). When Wii homebrew comes out, we will all be able to use a Wiimote/nunchuck/classic.