Here's what I'll do: I'll put together an Intel build and an AMD build around $500 (inclusive of shipping and rebates). I'll do my best to leave enough room for a hard drive and optical drive, but I'll leave those up to you (unless I find something attractive). Try asking your friends (possibly coworkers) if they've got any old laptops or they don't use anymore - even older laptops have SATA drives in them, so you may have luck finding one that way.
Intel
CPU:
Intel i3-2120 - $125
Mobo:
ASRock Z68 Pro3 Gen3 - $105
GPU:
Sapphire Radeon HD 6870 - $165
RAM:
Mushkin Enhanced Blackline 2x4GB DDR3-1600 - $45
Case:
Cooler Master Elite 430 - $40 ($30 with promo code; expires tomorrow)
PSU:
Corsair CX430 V2 - $27
Total - $507 + tax ($497 w/ promo)
Some combo deals I've found to knock some more $$$ off:
CPU + Mobo:
Intel i3-2120 + ASRock Z68 Pro3 Gen3 - $213
($17 off total)
CPU + HDD:
Intel i3-2120 + Seagate Barracuda 500GB - $188
($17 off regular) (HDD has $10 promo as well; dunno if it works with combos)
AMD
CPU:
AMD Phenom II X4 965 Black - $120 ($105 with promo; ends tomorrow)
HSF:
Cooler Master Hyper 212 Plus - $20
Mobo:
ASRock 970 Extreme3 AM3+ - $85
GPU:
Sapphire Radeon HD 6870 - $165
RAM:
Mushkin Enhanced Blackline 2x4GB DDR3-1600 - $45
Case:
Cooler Master Elite 430 - $40 ($30 with promo code; expires tomorrow)
PSU:
Corsair CX430 V2 - $27
Total - $502 + tax ($477 w/ promo)
Some combo deals:
CPU + HDD:
AMD Phenom II X4 965 BE + Seagate Barracude 500GB - $182
($18 off regular) (HDD has $10 promo as well; dunno if it works with combos)
CPU + HSF:
AMD FX-4100 + Cooler Master Hyper 212 Plus - $130
($10 off regular; $20 off total) NOTE: FX-4100 is a bit slower than 965BE; at a high resolution, it won't make a huge difference in gaming, but I'd stick with the 965 if I were you.
Mobo + RAM:
ASRock 970 Extreme3 + Mushkin EB 2x4GB DDR3-1600 - $122
($8 off total)
Mobo + PSU:
ASRock 970 Extreme3 + Corsair CX500 V2 - $122
($15 off regular; $10 more than total) NOTE: With the higher TDP and OCing capabilities of the Phenom over i3, you may want a better PSU. This is the same series as the 430W I suggest above, but pushes 500W instead.
If you need to take off more, you could look into downgrading the GPU some. Some alternatives could be:
XFX Double D Radeon HD 6850 - $135 (fastest of these 3)
EVGA Superclocked GeForce GTX 460 - $132 (not recommended)
Sapphire Radeon HD 7770 - $135 (less powerful than 6850/460, but draws significantly less power)
Final Notes
The 965BE is probably your best bet on an AMD processor from Newegg; however, if you're able to find a Phenom II X4 960T
elsewhere for $100-$140, definitely go for that over the 965; the [strike]Thuban-based[/strike] Zosma-based 960T has a better memory controller than the Deneb-based 965BE, it overclocks better, draws less power, and if you're lucky you'll be able to unlock two extra cores in the 960 (and a 6-core PII at $100-$140 is a steal).
Now, the Intel build may perform faster because Sandy Bridge is faster than Deneb/Zosma/Bulldozer. However, I'm not sure how long the LGA1155 socket will last past Ivy Bridge, so I can't comment on its lifespan. I do know Piledriver (AMD's next processors) will be AM3+ compatible, so you've still got that path to upgrade with on the AMD side.
The reason I included a heatsink/fan with the AMD build and not the Intel build is because the i3 can't overclock, so its stock fan will do just fine. The Phenoms, on the other hand, can overclock really well (and it's advisable that you do), but they also run pretty hot (being 125W chips).
The choice really is up to you - Intel runs faster, more efficiently; AMD is a bit more affordable depending on how you decide to work with it (not OCing might let you get away with the 430W PSU and dropping the Hyper 212).
Edit: Damn this post is big. Sorry. This was fun though.