but to answer you yes... you need a GC remote to play GC games... the GC remote will also play some of the virtual console games that you download,and so will the wiimote...
the only controller you dont "need to have" to play all the wii/gc games is the Classic controller for the wiimote... but it is a better controller setup for some VC games, and will be used alot more in future wii games as an option...