1. @Munkeh: 100% pure hardware bc. I could swear it even makes some games look a bit better
2. Well, the Wii does have 4 GC controller ports, and it would be pretty retarded if they did nothing, so...
GC controllers work for GC games, VC games, and even Wii games that are programmed with a GC controller option (mostly Wii/PS2 ports)
OT: I'd definitely go with the GC controller. The Classic Controller has to be plugged into a Wii-mote, meaning there's extra weight dangling around and it uses battery power. Never used a Wavebird so can't help you there.