Wii Mote and Nunchuck. I'd use a classic controller if I had one though, grew up with that gamecube controller playing melee. Dunno why people have trouble with Wii mote + nunchuck though, it's very simple to use but people seem to struggle and hate it :/
I use a Gamecube controller (Mainly because of Melee), but I have tried the wii mote (When I first bought brawl in 08 lol for about a few weeks).. It's just so confusing and hard to use... especially in competitive gameplay like I do. I attend tournaments and you rarely will see a wii mote user or classic controller. Gamecube is pretty dominant.
I actually like to use the gamecube controller in order to play. I don't like the tilt and move function, and sometimes I find the nunchuck doesn't respond fast enough for me. However, this is coming from an old school gamer, so it could all be in my mind..
I use the remote and nunchuck. I would use the GC controller but by the time Brawl came out I'd been out of melee for a while so I decided to go with the remote and nunchuck. I can use all styles though. I practice each one cause I've been to school tournies that don't have exactly what I want.
Wii Remote. I don't have the game, so I can't experiment with a Wii Remote and Nunchuck. But I can use a Gamecube controller. I've played Melee before. The controls are basically the same, so it's easy for me.