Ok here's a build. There was no way to work a monitor into it and make budget:
G.SKILL Value 4GB 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666) Desktop Memory Model F3-10666CL9S-4GBNT
Model #:F3-10666CL9S-4GBNT
Item #:N82E16820231423
$29.99 $29.99
There were a couple ways to do this. Normally I'd go for a two-stick kit to operate in dual-channel mode. That would populate both slots on a budget motherboard though, necessitating replacing them to add memory; this way you can buy another stick later. You'll lose a little performance, but not much.
GIGABYTE GV-N65TOC-1GI GeForce GTX 650 Ti 1GB 128-bit GDDR5 PCI Express 3.0 x16 HDCP Ready Video Card
Model #:GV-N65TOC-1GI
Item #:N82E16814125447
$129.99 $129.99
Not quite the cheapest one, but this GTX650Ti has a nice factory OC on it. I wanted to work a Boost Edition card into this build, but couldn't quite do it.
Athena Power CA-GSB01DA Black 0.8mm SECC Steel ATX Mid Tower Computer Case - OEM
Model #:CA-GSB01DA
Item #:N82E16811192289
$29.99 -$5.00 Instant $24.99
This case has 0.8mm steel, which is very solid for a cheap case.
ASRock B75M-DGS R2.0 LGA 1155 Intel B75 SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard
Model #:B75M-DGS R2.0
Item #:N82E16813157362
$54.99 -$5.00 Instant $49.99
This board has modern interfaces (USB3.0 and SATA 6Gb/s), but is otherwise very limited on expansion, with but a single PCI slot. This is probably the first piece I'd improve with a budget increase.
Antec VP-450 450W ATX 12V v2.3 Power Supply
Model #:VP-450
Item #:N82E16817371045
$49.99 -$5.00 Instant $44.99
A few weeks ago, this PSU was $10 less. It is still probably the cheapest one I'd buy though.
Intel Core i3-3220 Ivy Bridge 3.3GHz LGA 1155 55W Dual-Core Desktop Processor ...
Model #:BX80637i33220
Item #:N82E16819116775
$129.99 $129.99
Your specified CPU. Should be a good choice.
Western Digital WD Blue WD5000AAKX 500GB 7200 RPM SATA 6.0Gb/s 3.5" Internal Hard Drive -Bare Drive - OEM
Model #:WD5000AAKX
Item #:N82E16822136769
$59.99 $59.99
Seems to me I saw a deal on a 500GB Seagate for $10 less last week, but it probably required a discount code.
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.
Subtotal: $487.92
Shipping will likely use the rest of your budget. If you've got some wiggle room, the first thing I'd improve is the motherboard. The brand is fine, I'd just like one with a few more features and slots.
It would not surprise me if you could find one or more deals, shaving a few dollars off a few of these items. If you live near a Microcenter, they often have CPU+mobo combo deals.