Probably a dual core, 2gb ram, gts 220 or so. That'd be my guess...
Let's see, a quick delve into newegg... Don't need a hefty power supply, so you could get a case/supply combo for around $40, athlon x2 7850 processor for $50, ecs mobo for $55 shipped, 2gb ram for $40, 500gb hd for $50 shipped, bluray drive for $60 shipped, and actually, looking at 220 prices, 240's are only $10 more. You save a CHUNK when you drop down to a 210, but I'd have qualms about that doing well, so who knows. Assuming you get the 240 ($75) that puts you at around $375 (335 with a 210, but like I said...). No keyboard/mouse/os, assuming those are already owned. And you probably want to get a winMC remote as well.
In many cases you could squeeze by for less, but with nonsensical losses (ie, drop to a 160gb hd for $40 or switch to an open box mobo for $35).
That wouldn't be much use for games though. For that I'd say step up to quad core, double (or better yet quadruple) the ram, and get at least a gts 250 (or gtx 465 for better future proofing!). I also like to raid 0 my drives.