Nice job on a budget. Just a couple things to check; there have been some awesome deals on HD7870s lately. You may find one for not much more than the HD7850. The XFX ProSeries PSU will be able to run it, but the 550W version would be more comfortable, especially if you intend to overclock. Ignore these two things if it breaks your budget.
Check benchmarks for the [types of] games you intend to play. The similarly-priced GTX650Ti Boost Edition may offer slightly better performance.
You will likely want to overclock your FX-6300 for best results. The stock cooler will be loud at best, and simply insufficient at worst. I use and recommend the Xigmatek Gaia over the more often parroted but slightly inferior Hyper212 EVO: http://www.techreaction.net/2011/07/07/review-xigmatek-... http://www.techreaction.net/2011/11/27/review-cooler-ma...
Unlike the Hyper212 EVO (ignore the URL; it IS the EVO they tested), the Gaia never throttled. Although its price was recently jacked, the Gaia is generally a little cheaper too, making it a better deal all around.
This build is almost identical to mine. I really like the products you selected (duh, I selected them too), and I think you have done a good job so far. You could maybe go for a CPU cooler if you want to do any overclocking, and maybe find a 2 TB HDD if it's in your budget. Other than that, golden.