I tried playing with the Wiimote-Nunchuk combo in the beginning. And while that worked quite well, after playing Melee for like 7 years on the GameCube I just couldn't get adjusted. So I use Wavebirds. :)

Gamecube controller.

I've used all controllers and I have to say the GC and classic controllers are the best options.

The Wii remote doesn't have enough buttons, no c-stick, and moving with the D-pad is a pain. The Wii remote combo is better but the set-up makes it hard to do certain actions smoothly, but you have shake smash.

The GC controller is great, its pretty much the standard with serious players. The Classic controller is my controller of choice, though. It has a pretty similar set-up to the GC but as GhaudePhaede010 said it gives you the smoothest experience. Great for competetive use when you have to react fast. And the extra Z button is nice to have for when you are using personalized control schemes.

Classic controller all the way. Nothing else compares.

Wired Gamecube. Any other way is blasphemy.
(>'.')>

i'm so screwed now. i was playing with my gc controller, but it broke. i then resorted to playing ssbb with wiimote only, and when i finally bought a new gc controller, i suck with it, yet i can kick ass with tha wiimote.

sixaxis

now seriously, I never played SSBM but I find the GC controller WAY better than any other configuration. Sometimes I have to use de wii mote+nunchuck because there aren't enough GC controllers for everyone on my group. I can play with both, but GC is the best way to play it.

the wii mote alone is the worst in my opinion, some buttons are hard to push or are on a bad position (like the +, - or B) and I find missing buttons. Ok, you can do everything with combinations but its not the same.  Its playable, but...

wiimote only is the one ifeel most comfortable with

I play with the Wii remote + nunchuck. I tried the other schemes and they just are'nt as comfortable. IMO.

Gamecube controller. Only.