$600 budget build

That's not enough information to go on and provide you with a good answer.
Please re-post based on these guidelines: http://www.tomshardware.com/forum/353572-31-build-upgrade-advice

Thanks!

Yes, we need more information. Does he have a monitor? That question alone will make a huge difference. Keyboard? Mouse? Speakers? Etc....

Ok, here's an Intel build:

MSI N650ti-1GD5/OC BE GeForce GTX 650 Ti BOOST 1GB 192-bit GDDR5 PCI Express 3.0 x16 HDCP Ready SLI Support Video Card
Model #:N650ti-1GD5/OC BE
Item #:N82E16814127731
Mail in Rebate Card
$154.99 -$15.00 Instant $139.99
This card should get good settings on even recent games up to 1920x1080; estimated at "High Settings" by HardOCP in their review of the GTX650Ti Boost.

Intel Core i3-3220 Ivy Bridge 3.3GHz LGA 1155 55W Dual-Core Desktop Processor ...
Model #:BX80637i33220
Item #:N82E16819116775
$129.99 $129.99
Modern games are using more cores and more threads. I would not suggest a Pentium any more for new games.

ADATA XPG Gaming Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model AX3U1600GC4G9-2G
Model #:AX3U1600GC4G9-2G
Item #:N82E16820211457
$69.99 -$17.00 Instant $52.99
Although I prefer G.Skill, I've also had decent results from A-Data RAM in the past.

Athena Power CA-GSB01DA Black 0.8mm SECC Steel ATX Mid Tower Computer Case - OEM
Model #:CA-GSB01DA
Item #:N82E16811192289
$29.99 -$6.00 Instant $23.99
Surprisingly sturdy for a cheap case, and the price is great.

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
Very bare bones; this is probably the first item I'd improve with a higher budget, but in a budget build, it should get the job done.

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 -$14.00 Instant $45.99
Has been my "go to" PSU in budget builds for years. It will have no trouble with a GTX650Ti Boost, or even a GTX660.

Western Digital WD Blue WD5000AAKX 500GB 7200 RPM RPM 16MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive - OEM
Model #:WD5000AAKX
Item #:N82E16822136769
$59.99 $59.99
I've got a few of these. Other than one DOA (it happens), they've been trouble free.

LG 24X DVD Burner - Bare Drive Black SATA Model GH24NS95 - OEM
Model #:GH24NS95
Item #:N82E16827136259
$17.99 $17.99
One optical drive is much like another.

Subtotal: $520.92
A hair over, but there is a rebate on the graphics card. Have some peanut butter & crackers for lunch a couple times instead of going to McDorkles.
There's not too much to cut out of this. Although I'd prefer a nicer mobo, there isn't anything here I would not buy myself (or I could not suggest someone else do so).
Someone will probably suggest an AMD build at this price point, which will probably also be worth considering. The types of games your friend plays may influence any tweaking of relative strength between the CPU and GPU.

The FX-6300 is a viable option, especially when overclocked. The GTX650Ti Boost is a LOT stronger than the HD7770 though (even the vanilla GTX650Ti is), and even though it is smaller, the Delta-built 380W Earthwatts is higher quality than the CWT-built Corsair CX.
Asus is a good choice, but I'd get a newer, 900-series chipset board, with heatsinks on the VRMs, especially since you will most likely overclock it at least some.