There is a post in the sticky section about what speed computer you need for MAME... check that out. You can play classics with something like MAME .55 on like a 400mhz computer or so, most games on say a 800mhz - 1ghz machine, and above that you add a few games at a time, with some just not playable with today's computers.
As for a video card, MAME is not video card intensive AT ALL... the CPU is much more important. You could get the cheapest card with Svideo on it and be fine. If you're using an arcade monitor, use an ArcadeVGA, but with a TV like you mentioned, basically any TV-out card will be plenty if you are only using MAME.