If you play Gamecube games on the Wii, do you need a Gamecube memory card, or can you store the save games in the Wii memory?

Thanks

I have a Wii and was going to buy some second hand Gamecube games. Do I need to buy a Gamecube controller, or does the Classic Controller have GC functionality? I am assuming I need to buy the GC controller, but thought I would check before making a purchase.

 Thanks.