The Classic Controller and the GCC are your only two real options if you don't want to be limited by your controller. The C-Stick is absolutely crucial. There are techniques that cannot (reasonably) be performed without it. As someone who used the Wii/Chuck for a long time before getting a CC, I can assure you that none of the possible Wii/Chuck configurations adequately simulates the functionality provided by a C-Stick. (This includes using the D-Pad for Smashes.) Just spare yourself the trouble and get a CC or a GCC.
Be aware that the Classic Controller has an extra shoulder button, which can be extremely helpful for certain characters. It also allows for slightly greater flexibility when configuring your control scheme.
Also be aware that the Classic Controller suffers from wireless interference, which can be a huge problem. In fact, since I've started playing Sheik and working on mastering her Chain, the large amount of wireless interference my CC gets has become painfully apparent. It's to the point where I spent a great deal of time trying to find a non-wireless version of the CC (which apparently doesn't exist), and if the situation doesn't improve soon I'm probably to going to get a GCC instead. I will sorely miss the extra shoulder button, but the wireless interference makes it impossible to keep Sheik's Chain deployed consistently as even the slightest moment of connection loss results in her putting the Chain away.
The GameCube Controller is also much simpler to handle because it doesn't require tedious battery management and getting connected to the proper controller port is much easier with a GCC.
Either way, the CC or the GCC are both great. Using anything else hurts you.