Everyone else has already answered the red and white wire problem. So I figured id answer a question you didn't ask for! 😎😎😎
The yellow wire is composite video. This is easily the worst option for these consoles, I'm sorry to say you lost out.
Svideo and Component are easily the better, readily available, options and make the video look better.
Although the best setups for each respective one is:
Ps2 (fat) - Component | nearly completely backwards compatible with all PS1 Games. Not emulation.
GameCube (Must have Digital Out port) -
Carby V2 | reasonably priced HDMI adapter compared to it's competitors and the component cable.
Wii U - Default | The Wii U is backwards compatible with the Wii and has a native HDMI output. As far as I'm aware this is not emulation and is running on real hardware. However, much liker later Wii revisions, you can't play GameCube games natively.