If you want to have the games on Wii U menu like the OP, you have to install them on a HD (which will use Wii U own file system, so it won't be compatible with other devices). Unfortunately, you can't install them on SD card. If you want to use a SD card, you can put there the Wii and GC games and launch them using a Wii USB Loader/Nintendont. GC games will still be compatible with the GamePad (if using the latest version of Nintendont), but sadly the Wii games won't.
Personally I suggest going the external HD route. Keep in mind you'll need a HD with a Y cable or an external power source. A 250-300 GB one is fine for a nice GC-Wii-WiiU library. As for the memory card, since you have to copy the games there first to install them on a HD, I suggest at least a 32GB one.
Yeah, both Nintendont (if you want to play them from SD card) and TeconMoon's
Injector (if you want to convert them to Wii U installable package) support those extensions.
Yes, if you use the Injector, you can play with the GamePad every Wii game which supports the Classic Controller or the WiiMote without motion controls. Games which uses the Nunchuck (or the Wiimote pointer/gyro/accelerometer) can't be played with the Gamepad, sadly.