if you're very worried go ahead and get the 8 core 8320, but I think your GPU would bottleneck before the CPU would. The fx6300 is really good for the price. If you're not happy with the performance of the 8320 it's not the end of the world, at that point, just save up for an i5 cpu and motherboard, only you yourself can know for sure if you won't be happy with the cpu. The gpu matters more for games anyway. Getting a better gpu like gtx 760 or 770 would make more of a difference.
If that's too much money for you, just keep what you have and chill and enjoy your new pc, you could certainly do MUCH worse out there than a 4ghz 6 core cpu and r9 270x gpu