FX 6300 is only a 3 core processor featuring 6 threads, while FX 8320/8350 is a 4 core processor featuring 8 threads. More cores are better in gaming, as the latest games support more cores, even threads.
The boost clock of the 3 are much alike.
FX 6300 FX 8320 FX 8350
3.5 GHz (4.1 GHz boost) 3.5 GHz (4.0 GHz boost) 4.0 GHz (4.2 GHz boost)
So, the best choice in my opinion is FX 8320, because it's cheaper than the FX 8350 while offering similar performance and with the money you save, then you can buy a better cooler, that will allow you to overclock it better.