Do you already have a monitor, keyboard, mouse, and Windows license? As having to get all of those parts really effects the type of rig you can build for the money.
Anyways the best I can figure is about $865 shipped for a good gaming rig if you need all of these parts.
CPU -
Pentium Dual-Core e5300 (Fast, Cheap, good overclocking ability with stock fan/heatsink)
GPU -
Powercolor ATI Radeon 4870 1GB (should be hackintosh compatible, good cooler design, powerful)
MB -
Gigabyt GA-EP43-UD3L (good reviews, good for overclocking, plenty of expandibility, confirmed as working with Mac OS X Leopard install on InsanelyMac.com)
RAM -
4GB DDR2 1066mhz (to give you room for a decent overclock without fiddling with the multiplier)
HD -
500GB Seagate Barracuda (Good and quiet hard drives)
DVD -
DL DVD Burner
Case -
Rosewill (cheap and quiet because of 120mm fan, hopefully)
PSU -
XCLIO 500W (Good reviews, 2x6 Pin molex, though I would spend more for a 80+ certified PSU)
Mouse-
Logitech MX310 (cheap, great for gaming, I have used this for about 4 years now, OS X drivers for extra buttons)
Keyboard -
Microsoft Comfort Curve 2000 (cheap comfortable keyboard, OS X drivers online for media keys, have owned 2+ years)
Monitor -
Acer 22" (good sized, resolution, DVI, reviews)
Windows -
Windows 7 Home Premium x64 (the RC has worked great for me even on old games)
You might be able to knock it down to $800 with DDR2 800 RAM, Pentium DC e5200 and a 19 or 20" LCD (make sure it has DVI). But try to avoid a cheaper Radeon 4850 as not all are Leopard compatible some do not work with any modified kexts. If you go for a cheaper GPU try to get one with at least 1GB memory.
Since you can swing $800 I would say don't cheap out and save the extra $65.
Also do you have a Leopard/Snow Leopard disc already? You would need to buy that too which will mean spending more or dropping the computers quality extensively.