I tried putting your ideas together, so how's this?
CASE: ANTEC THREE HUNDRED - $58
PSU: COOLERMASTER EXTREME POWER PLUS 650w - $90.09
MOBO: ASRock Z77 Extreme 6 = $209
CPU: (COMING SOON) (CORE I5-3570K) IVY BRIDGE - $225.00
RAM: G.Skill Ripjaws (2x4GB) DDR3 = $51.79
HARDDRIVE: WESTERN DIGITAL GREEN 1TB - $96.31
DVD/CD: LG DUALLAYER DVD BURNER SATA - $24.86
GFX: SAPPHIRE ATI HD 7870 GHz EDITION PCI-E - $364.83
MONITOR: SAMSUNG 24'' S24B300H LED - $186.95
TOTAL: $1306.83
Well you've come a long way from the system provided in your OP. This is much better.
First and foremost, just make sure that G-Skill RAM is compatible with the motherboard. If you haven't, go to the manfacturers site to check. You don't want to be putting in memory that isn't compatible with the M'board.
If I was to purchase this system, I'd go for the 7850 version of the Sapphire Card you chose. Only because of 2 reasons;
1. Your saving $85.00. Whilst the 7970 benchmarks are higher then that of the 7850, I think it's debatable if the extra $85.00 justifies this.
2. If you get the 7850 instead and are unhappy with it. You can simply purchase a 2nd one later on to run both in crossfire. But I think the 7850 alone will easily satisfy you enough tbh.
Lastly, the ASRock Z77 Extreme 6 Motherboard. I can't remember for the life of me why I didn't choose to go for that M'board now. This is a step up from the Extreme 4 in my build, however there is a reason why I didn't choose it (wish I could remember now). Just check the reviews on it to make sure you will be happy with it. Also, type in "ASRock Z77 Extreme4 vs ASRock Z77 Extreme 6" into google as well to see what other people think about it. Keep in mind, the Extreme 4 version is also $40.00 cheaper.
Overall, you can save $125.00 on this build easily without really sacrificing anything. You could use that money to upgrade the CPU to a Core i7-3770k Ivy Bridge. However, that is a good build.
Even the smallest donations help keep sc2sea running! All donations go towards helping our site run including our monthly server hosting fees and sc2sea sponsored community tournaments we host. Find out more here.