Ok, here's a build. I've commented under most of the parts what I think of them.
LG 24X DVD Burner - Bare Drive Black SATA Model GH24NS95 - OEM
Model #:GH24NS95
Item #:N82E16827136259
$17.99 $17.99
Meh. One optical drive is much like another.
Athena Power CA-GSB01DA Black 0.8mm SECC Steel ATX Mid Tower Computer Case - OEM
Model #:CA-GSB01DA
Item #:N82E16811192289
$29.99 -$7.00 Instant $22.99
Dirt cheap case, but supposedly made with 0.8mm steel, which is pretty thick. Most cheap cases are much thinner.
Intel Core i3-3220 Ivy Bridge 3.3GHz LGA 1155 55W Dual-Core Desktop Processor ...
Model #:BX80637i33220
Item #:N82E16819116775
$129.99 $129.99
This hyperthreaded CPU should remain fairly competent in games for a good while, although multi-player BF3 may make it sweat a little.
SAPPHIRE 100358L Radeon HD 7770 GHz Edition 1GB 128-bit GDDR5 PCI Express 3.0 x16 CrossFireX Support Video Card
Model #:100358L
Item #:N82E16814202011
Mail in Rebate Card
$119.99 -$5.00 Instant $114.99
There's a fat rebate on this one, if you play that game and win. More important, the HD7770 is a decent card on a tight budget. This is something to improve if your budget allows though, to a GTX650Ti or HD7850.
ASRock H77M LGA 1155 Intel H77 HDMI SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard
Model #:H77M
Item #:N82E16813157303
$74.99 -$5.00 Instant $69.99
Solid non-overclocking board, suitable for the locked CPU. I just used this board in a build for my father, and it's fine.
Antec VP-450 450W ATX 12V v2.3 Power Supply
Model #:VP-450
Item #:N82E16817371045
$49.99 -$10.00 Instant $39.99
Efficient enough for 80+, disqualified only because it doesn't have full range active PFC. This is perhaps the cheapest PSU I'd buy myself, and can handle a HD7850 if you get the stronger card.
G.SKILL NS 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10600) Desktop Memory Model F3-10600CL9D-4GBNS
Model #:F3-10600CL9D-4GBNS
Item #:N82E16820231394
$26.99 $26.99
8GB would be nice, but on a budget this will have to do. You'll lose some performance, but may wish to consider a single 4GB stick now, and add another stick later.
Western Digital WD Blue WD5000AAKX 500GB 7200 RPM SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive
Model #:WD5000AAKX
Item #:N82E16822136769
$79.99 -$20.00 Instant $59.99
Although I prefer the longer warranty of the WD Black, I've got a few of these out there that have been fine too.
Subtotal: $482.92
Add another $90 for the OS, and you're right around budget, especially with shipping.