I'm going to use the Retro Incabulator.
[youtube]http://www.youtube.com/watch?v=TuhYd9L_d7w[/youtube]
sorry... couldn't resist
Seriously though, if your just going to be using MAME, one thing to know is that a graphics card is more or less not a factor. MAME is almost entirely processor dependant. Furthermore, if you're only going to be playing classic games in MAME, an old PC will probably be good enough... as old as 8-10 years old.
However, if you are going to be playing any games from 1990 on, your going to need a computer with a little more oomph. And if you're going to be playing recent 3D games, your going to need a brand new PC with a state of the art processor to play them without slowdown.
Also, If your going to be using other emulators besides MAME, a decent graphics card will be needed for any emulator that plays 3D games.