Ya know what's weird, I have a 333mhz celeron piece of crap right, but we got 256mb of SDRam and I'm running Memturbo to free up resources, I'm thinking not only does ram have something to do with it, but your video card has a big part to do with it. Buy a video card that doesn't support 2d games, no 2d games, buy a card that has good 2d hardware, Mame will run no problem.
BUT I'm thinkin anywhere in the range of 1ghz and 256 or 512 mb of ram, and you're computer's gonna run any game in MAME no problem, just don't get an off-brand "Powered By" video card, they might be cheaper, but in the end, that extra money for the "Built by" is definitely worth it.
-CthulhuLuke