I second that X-ray, I have an A1200 with a Blizzard 1230 card, 32mb ram. Really great setup for Games using WHDload, does some other things too, and web browsing works... just need to be patient :-)
That said if you want more than games, an Amiga 4000 would be a better option, providing you don't mind spending the cash... the upgrades aren't cheap...
Robert
