I have $600 to spent on a gaming pc,
I want it to be able to play Mass Effect 3,BF3 and Skyrim
On ultra at 1600x900 res and work well with my 5.1 speakers
(I have monitor, keyboard, mouse, speakers,a spare
60gb SATA HDD, spare win 7 64 bit, blu ray drive and a case)
Oh and I have a spare 6770
At that resolution, I would guess the HD6770 would be able to play on high settings, but probably not ultra. Here's one way to do it:
ASRock Z68 PRO3 GEN3 LGA 1155 Intel Z68 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard
Model #:Z68 PRO3 GEN3
$114.99 -$10.00 Instant $104.99
Won't allow for multiple GPUs, but it's future-resistant otherwise, with 4x RAM slots, USB 3.0 and SATA 6Gb/s.
G.SKILL Value Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666) Desktop Memory Model F3-10666CL9D-8GBNT
I've had good results from G.Skill. This low-cost kit uses Micron chips. You could get by with 4GB, but at half the RAM for more than half the cost, I think this makes more sense.
SeaSonic M12II 520 Bronze 520W ATX12V v2.3 / EPS 12V v2.91 SLI Ready 80 PLUS BRONZE Certified Modular Active PFC Power Supply
Model #:M12II 520 Bronze
$99.99 -$20.00 Instant $79.99
There are other choices here, but this one is solid, modular, and efficient. Get something bigger if you might get a much more powerful GPU in the future, but note that AMD's 7000-series use LESS power than previous generations; I expect Kepler will be similar.
XFX Double D HD-687A-ZDFC Radeon HD 6870 1GB 256-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card with ...
Mail in Rebate Card
$189.99 -$20.00 Instant $169.99
I could not quite fit a GTX560Ti into your budget, but this card should be able to play with Ultra settings at your resolution.
Intel Core i3-2120 Sandy Bridge 3.3GHz LGA 1155 65W Dual-Core Desktop Processor Intel HD Graphics 2000 BX80623I32120
I wanted to fit an i5 in here, but that also breaks the budget. This CPU will do well.
Samsung by Seagate Spinpoint F3 HD502HJ/ST500DM005 500GB 7200 RPM SATA 3.0Gb/s 3.5" Internal Hard Drive -Bare Drive
$89.99 -$5.00 Instant $84.99
60GB isn't enough, by a long shot. This is more like it. You can always add a SSD later.
Subtotal: $605.94 (but there's a rebate in there, and I think some % off codes)
These were not the cheapest options, but I'd like to think they are fairly future-resistant. Sacrifices on the mobo (like H67 or even H61) would allow you to fit the GTX560Ti into this build, but then you'd never be able to OC (making an upgrade to a "K" series CPU pointless). AMD has been late with Crossfire support in new games, so running a pair of HD6770s did not strike me as viable.