well for a FX6300 a 6+2 powerphase is totaly fine.
The Msi 970A Gaming is basicly a very good board for its price.
The Asrock Extreme 9 is offcourse one of the top ends boards wenn it comes to AM3+. But i think for a FX6300 that would be a bit of a waste to be honnest.
The Msi 970A gaming is arround $100 mark or something, which is totaly a fine board for that cpu. He could spend the extra $70 on a better gpu.
I was personaly thinking about a locked i5 with some cheap H97 board or what not, Because the better single threaded performance realy benefits in cpu bound games like skyrim, But this highly depends on the games that "op" is playing,
An FX 8320 will overclock to a point in which it will outperform an i5 for half the cost. It's nearly as good as an i7 in multithreaded applications. If he needs a better board it isn't too hard to drop $10 more. Yes, a GTX 770 would greatly outperform an R9 270x however they are roughly $50-60 more. I understand his case as I am building my first rig and have to fit it under $350. To give you an idea, I will have 24 threads! A single stick of RAM is neccasary as he will later be able to upgrade to 32gb instead of a lacking 16gb. If you can find one, R9 290xs go for around $250 on eBay which definitely outperform a 770.
An FX-8320 won't overclock and get performance past an i5(esp. not a Haswell i5), especially because of AMD's changed binning procedures - FX-8320's aren't as great of overclockers as they used to be.
Also, you can overclock an i5 as well. Just because you can overclock one chip to match the stock speeds of another doesn't mean you can't overclock the other chip.
R9 290Xs will indeed outperform a GTX 770 - just make sure you have a power supply to handle it.
The second option is definitely worth the money.. Here is another option
$490 - http://pcpartpicker.com/p/kW2Lbv
Better CPU and the better graphics card, but less ram... but that can be upgraded later for not much more... and honestly you can get by on 4gb of ram for most games. This will give you better CPU performance with better graphics performance. The CPU improvement is worth the ram reduction, because you can upgrade later when you really need it for a low cost.