What's the cheapest way to get into GameCube and Wii emulation?

[Glen707]

I want to emulate these GameCube and Wii games at either 720p or 1080p (and be able to output to a TV via HDMI);

New Super Mario Bros
Super Mario Galaxy 1& 2
Super Mario Sunshine (with Skip EFB Access disabled so goo works properly)
Pikmin 2 (GC)
Twilight Princess (GC) & Wind Waker (GC).

I don't care if it's based on windows, Linux, or a custom OS for emulation specifically. I just want a dedicated machine for the cheapest price. Any suggestions?

Thanks!