A Wii or Gamecube, a copy of Brawl or Melee, an SD card and basic technical knowledge to load Project M.
If are looking for a computer and want to play Smash competitively, don't. One plays Smash competitively by attending tournaments in person in their region usually. Those are played on consoles, not computers.
If you are still dead set on a computer, I really can't help. What I do know is that my 300 dollar laptop with a garbage integrated graphics card can emulate Melee at 60 FPS with a few tweaks.
Seriously though, just get a used Wii (make sure it has Gamecube ports). I got mine two years ago for $45 dollars. Far more cost effective than buying a good computer.