Best way to get better is to play against other real people. For tech, I'd definitely try to get 20XX Melee any way possible. Though Dolphin has quite a bit of input lag, unless you use the official adapter from Nintendo or possibly the new one Mayflash created then the input lag becomes less noticeable. For Gamecube, you're gonna have to do some modding, physically to be exact, if you want 20XX on it. I'd probably go with 20XX on Dolphin though for a few reasons, CPU random DI, flash on L-cancel or red flash when failed to L-cancel, single player mode, and forced Sheik CPU if you want to practice on Sheik if you ever need to practice comboing her. Though ideally you'd want 20XX on a console, Wii, Gamecube, or Wii U, if you have the Gamecube adapter for Wii U, all work.
EDIT: Yea play on CRT if you can, high end gaming monitors and EVO monitors are a decent choice too, but CRTs have lowest input lag possible. CRTs are cheap too, so might as well. Just NEVER play on an HDTV, those are the absolute worst option for Melee. High end gaming monitors and EVO monitors have input lag, but it's only noticeable at the highest technical level play, since the input lag is below 1-frame or maybe even below .5 frames. Don't be super discouraged if a gaming monitor is your only choice, I'd still try to get a CRT though. If a low input lag monitor is your only option though, don't be surprised if people doesn't go to your place to play Melee, so you'll have to go out to play instead.