It is my humble opinion this system is heavily limited by your budget. While this will probably be adequate depending on what sorts of games you are wishing to play and in what quality settings, it is my opinion you would ultimately be happier if you saved some more money to have a better budget. But if this is not possible, this is what I can do for you:
CPU- Phenom II 720 tri-core $80. In my opinion this is superior to the similarly priced i3s (one man's opinion, however does not make a fact the i3s are dual cores, most modern games call for quad cores even though games as of today do not effectively use more than 2)
http://www.tigerdirect.ca/applications/SearchTools/item...
Fan and heatsink (as its not included with that CPU) -$30
http://www.tigerdirect.ca/applications/SearchTools/item...
There are better fans on the market, this is not a great one, but it is sufficient. Being that I recommended a "Black Edition processor", which denotes that their multiplier is unlocked for easier overclocking, it may be worth spending a few more dollars for a better fan and heatsink to turn up the multiplier on that CPU to make up for its lacking stock performance. Black editions are made for overclockers.
Motherboard- MSI 760GM-P23- $60 Very bottom of the barrel for this brand, but MSI is a very competent manufacturer.
http://www.tigerdirect.ca/applications/SearchTools/item...
RAM- Patriot 8GB kit- $30
http://www.tigerdirect.ca/applications/SearchTools/item...
Graphics- GTS 450- $110 Not my favorite card on the market in terms of performance, but it does at least use GDDR5 RAM for the memory, which is the latest version
http://www.tigerdirect.ca/applications/SearchTools/item...
Hard Drive- Seagate Barracuda 250GB- $70
http://www.tigerdirect.ca/applications/SearchTools/item...
Case Basic, didn't even notice the brand- $36
http://www.tigerdirect.ca/applications/SearchTools/item...
Power supply Corsair Builder Series 430watt- $20-
http://www.tigerdirect.ca/applications/SearchTools/item... I don't recommend cheap power supplies, but you can look at my Member Configuration to see what brand I trust to power my systems.
CD Rom/DVR-Writer[/b] (use your old one to save a couple bucks) $18-
http://www.tigerdirect.ca/applications/SearchTools/item...
Total cost: $454
Finally, you'll still need an operating system. I'll leave that decision to you, as it puts you over the stated budget. I personally got Windows 7 for free through my college, so it doesn't get figured into my $912 system that I mentioned to you earlier. Maybe someone else can quote you on a cheaper system with better/similar features, so don't rush off and buy parts yet.
Edited due to original quote having inadequate power supply/case combo.