Ok here's a build. The budget imposes limitations, but this is NOT a bad little system:
ASRock M3A770DE AM3 AMD 770 ATX AMD Motherboard
Model #:M3A770DE
Item #:N82E16813157176
$59.99 $59.99
Bulldozer was not worth it, so AM3+ is an unneeded luxury; was an easy sacrifice to the budget. This mobo became a standby in budget AMD builds. I've used a couple of them myself with no problems. You do give up USB3.0 and SATA 6Gb/s but you'll need to spend another $30 to get those.
Antec EarthWatts Green EA-380D Green 380W Continuous power ATX12V v2.3 / EPS12V 80 PLUS BRONZE Certified Active PFC Power ...
Model #:EA-380D Green
Item #:N82E16817371033
$59.99 -$30.00 Instant $29.99
Excellent deal on a very solid PSU. Will handle a HD6850, but nothing more; does put a cap on future-resistance, but again that shouldn't be a problem.
Acer S201HLbd Black 20" 5ms LED-Backlight LCD monitor
Model #:ET.DS1HP.001
Item #:N82E16824009256
$139.99 -$50.00 Instant $89.99
Yes, there is a 1920x1080 monitor available for the same price, but you might be straining the GPU a little as it is, and this 1600x900 model seemed a reasonable compromise.
HIS H667F1GD Radeon HD 6670 1GB 128-bit GDDR5 PCI Express 2.1 x16 HDCP Ready Video Card with Eyefinity
Model #:H667F1GD
Item #:N82E16814161375
$97.99 -$8.00 Instant $89.99
You could drop back to a HD5670 for about $20 less, but I think a gaming PC needs as strong a GPU as you can get (within reason). Do that if you have to, but I would NOT drop either back to a GDDR3 model.
Seagate Barracuda 7200.12 ST3500413AS 500GB 7200 RPM SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive
Model #:ST3500413AS
Item #:N82E16822148701
$44.99 $44.99
That price is only valid in a combo, in this case with the RAM.
G.SKILL Ripjaws Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model F3-12800CL9D-8GBRL
Model #:F3-12800CL9D-8GBRL
Item #:N82E16820231314
$39.99 -$10.00 Instant $29.99
More than needed, but it combos with the HDD to save a LOT of money. In my experience, G.Skill is excellent RAM, it just works.
Rosewill Blackbone Black Steel / Plastic ATX Mid Tower Computer Case
Model #:Blackbone
Item #:N82E16811147023
$49.99 -$10.00 Instant $39.99
This case only has $5 shipping, so it works out to be an even better deal than it looks. I've built in this case, and it is roomy, and the fans are quiet but effective.
AMD Athlon II X3 445 Rana 3.1GHz Socket AM3 95W Triple-Core Desktop Processor ADX445WFGMBOX
Model #:ADX445WFGMBOX
Item #:N82E16819103872
$74.99 $74.99
May unlock, and can play any game (particularly on reduced settings) even if it doesn't.
Sony Optiarc CD/DVD Burner Black SATA Model AD-7261S-0B LightScribe Support - OEM
Model #:AD-7261S-0B
Item #:N82E16827118040
$19.99 $19.99
One optical drive is much like another, but this one has lightscribe.
Subtotal: $479.91
There you have it. Especially at the reduced settings you are willing to accept (but may not even need with the older games you've listed), this machine will perform decently. If you want to hold out until you can spend more, the places you'd want to improve first are the GPU (HD6770 or HD6850 without a PSU upgrade; anything higher will need a stronger PSU too) and possibly the CPU (the 955BE is $105 right now, but you'll also want a $30 cooler to overclock it decently).
Do not buy the apparently higher wattage HEC PSU that someone linked; the little voltage switch gives it away as, at best, an older, overrated, inefficient design; at worst a cheap system-killer.
If you can spend $550, a good case can be made for an Intel system for significantly more CPU power and a better upgrade path (though still not a great one).