Here's some additional info just because I'll be gone tomorrow
When do you plan on buying the parts?
Do you plan on making it upgradable?
http://www.tomshardware.com/forum/312913-28-intel-2100-phenom
http://www.hardwarecanucks.com/forum/hardware-canucks-reviews/44339-intel-core-i3-2120-core-i5-2400-lga1155-processors-review.html
Basically you will be choosing between i3/phenom x4, if you find something better though go for it.
Both around the same price range. Personally I've heard good and bad about both so you'll just have to do some research. In my own findings the i3 is better. Nice thing is that at newegg no matter which one you pick, all i3/phenom x4 have free shipping.
If your not planning to upgrade later on, then you can minimize on some things.
I made a build but it's $600 instead of $500 :S. I added in somethings that I thought would be beneficial for your system.
i3-2120 Free Shipping
ASRock H61M-VS Free Shipping
Patriot Gamer Series 8GB RAM Free Shipping
Antec 550w Free Shipping
Radeon 6580 Free Shipping
Seagate Barracuda 1TB HD $6.29 shipping
Lian Li Case Free Shipping
LG 22x DVD Burner Free Shipping
Total=$581.92
I hope you are able to get the Free Shipping! I'm not sure if taxes were included either.
I'd keep the i3/ASRock H61-M/Lian Li Case for sure. The 6850 would be a great addition, but if need be you can downgrade it. Also, the DVD burner is he cheapest I could find with good quality/free shipping.
Things you do to reduce the price in my suggested build:
Ram: I went for 2x4gb, but 2x2 will be $10-15 less.
Power Supply: You can probably find one for less(maybe $50) like in the build links I gave before. Personally, I wouldn't go much lower if any, because the PSU is a really important part of your build. I tried to cheap out on one during building my computer and I'm paying for it now because it doesn't work correctly
You will need to stay in the 450w or more range if you keep the 6850. (it says in the Details on the product)
Hard-Drive: You could find a 500gb for $20 cheaper, maybe $30 if lucky. I just figured that you get x2 the space for not much more in cost.
Graphics card: Not sure on the "next best", so you'll have to find out for yourself.
GPU Comparison
Reducing to 2x2GB RAM/500GB/PSU would save you around $50-$60. The RAM/HD/PSU are things you can always upgrade later. So you'd be at around $521.92-531.92.
I've put in enough suggestions for one day though :lol:
If you REALLY had to be close to budget, then in order of things to get cheaper:RAM,HD, graphics card then lastly the PSU.
Hope this is enough info for you, Have fun!