Well, here is what I did in December 2005. I had to buy a monitor (Dell 2005FPW) so my budget was a bit more than yours but I think you will like it.
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Motherboard:
Asus A8N SLI AMD Socket 939. My mobo works fine but from what I have read these boards may have overheating problems with the chipset. So do not get this board. Asus makes a good board so opt for the Deluxe or Premium version instead. The Premium is $168 from Newegg.
CPU:
AMD Athlon 64 3700+. As mentioned above, the 3700+ is a great bang for the buck option right now. $212 from Newegg.
Case and power supply:
Antec 640B Performance Case with 400W Antec power supply. Additional cooling provided by
Antec 80mm blue LED fan. The blue LED fan is $7 extra, sold separately. You will need to upgrade to a 500W power supply if you want to go SLI in the future. Otherwise, any 400W+ power supply from Antec, PC Power & Cooling or another reputable maker will do. $99 for case and power supply.
[NOTE: the Antec case does not come with hookups for the "hard drive activity light" if you are using a SATA drive. If you are using an EIDE/IDE/Ultra drive, then you're fine with this case. If you go with a SATA hard drive, as I did, you will just have to do without the hard drive activity light.]
Video card:
XFX GeForce 7800 GT. This was just under $300 w/rebate but for a gaming machine you should not skimp on your vid card. I also see that Newegg no longer has the XFX 7800GT in stock. If the 7800GT is too much, check out the 7600GT which can be had for around $170 after rebate. Check out the link to a Fatwallet.com thread below.
Memory:
Corsair 1GB (2x512MB) 184 pin RAM. Now down to $68. Not the fastest memory in the world but to me it doesn't make that much of a difference b/c I'm not overclocking. If you want to upgrade anything on this system, I'd do it here (maybe more or faster memory).
Hard Drive:
Western Digital 320GB 7200rpm SATAII. Again, a rebate deal. This one is $140 but I'm sure you can find a 250 GB SATA drive for cheap.
Optical Drives:
NEC dual-layer DVD R/W and
Lite-on DVD-ROM drive. I can't recommend the Lite-On drive any more because it is noisy as hell. The NEC burner is a great deal at $43. The Lite-On was $20-25.
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Total budget with the above is around $1100. If you ramp down to the
eVGA GeForce 7600GT (click on the link to see how it is $165 after rebate) and a
250 GB Western Digital SATA hard drive for $90 you can get your total cost below $870.