Mayflash is usually the way to go.
Gamecube controllers take a bit of setup, but there are guides everywhere on how to do so.
I personally prefer the Pro Controller. Just flip a switch on the side of the adapter and you're using Xinput. Pretty much no setup.
No, you are unable to use that adapter to play Project M on a WiiU with a Gamecube controller as of now.
I believe you are able to use this adapter. I really wouldn't recommend getting that though, since playing wireless isn't optimal. Also, if you remain hopeful, we may end up getting a method to do the whole PM + WiiU + Mayflash adapter + GC Controller setup. That depends on the WiiU modding community making strides in that department, though.