We will note that the Wii U isn't compatible with the GameCube controller, which means GameCube game controls are remapped to the Wii U controller. Here are all the platforms with titles available through the Virtual Console.
Thanks to the Wii U Virtual Console system, you can actually enjoy backwards compatibility beyond just Wii games.
WII U BACKWARDS COMPATIBLE UPDATE
When you're ready, make sure your Wii U has the latest system update and then connect both it and your Wii to the internet, and follow these steps: