balls up and get the mayflash usb to gamecube adapter for your PC.
both of my mayflash gamecube adapters broke relatively soon and were kinda unstable so i just recommend the wii u gamecube adapter since you can use it on smash 4 too
plus i imagine it works better with dolphin
(on the other hand, my mayflash classic controller adapter is perfectly stable and has worked for quite a while)
then get 20XX, a mod for melee that plays the game at a more streamlined approach (no intro sequence, auto puts 4 stock no item matches and highlights the tourney legal maps)
you could just use community netplay build (which has lagless FoD and a no-transform pokemon stadium, but maybe 20xx has it too i don't know) or the community netplay gecko code for the automatic settings
20xx has a lot of useful toggleable training features like random cpu DI/teching though so you should get it anyway