Buy or Build? -- Depends on what you feel comfortable doing -- knowing that you will get more comfort the more you try to build. Me, I would ALWAYS build given the choice.
In fact, the fun is in the building (and adding on) than the playing half the time.
Just plan it out ahead of time and know what you want -- lurk these forums for awhile, get some good ideas.
Joysticks -- I bet for the 2-d fighters you'd be happy enough with any 8-way joy. Happs Super or some such.
Low end Comp vs Xbox? Depends on how "low end" you mean vs what you want to run. I was able to run acceptable older versions of a LOT of 2d fighters w/ just a PII 300 and 512MB SDRAM, 32MB video card , win98 for awhile... but am much happier now w/ another "low end"

1.8GhZ P4. If by low end you mean somebody's garage sale P90 , you could probably still run, but not as much and you wouldn't be happy w/ it.
Get a mid-high end PC...