The only limitation I know of is that you need a GC controller to play GC games. As far as I've ever been aware, the North American Wii is compatible with all
GC games for the North American market.
You could run into region-lock issues, but those games wouldn't be compatible with your GC either. You may also run into some unusual peripheral compatibility issues, but you won't run into issues with the games themselves. Certain regions (Europe, I think) also have much more limited backwards compatibility with GC games (for copyright reasons, I believe). And, of course, any "unofficial" GC releases won't work on your Wii.
Otherwise, they should all work with no issues whatsoever (unless you're in a BC-limited region