This is our thinking on motherboards.
http://www.tomshardware.com/forum/id-2384030/motherboard-tier-list-am3-chipsets.html
The motherboard you have might fit the FX 6300 or FX 8300, but it lacks the power phases and VRMs and heatsinks (VRM =Voltage Regulation Module) to run those chips reliably. The motherboard is very likely to overheat and - worst case : fail, - best case: run slowly or thermally throttle.
The CPU you have now is about the best under $100 CPU that can be supported by the board. Sooner or later, you need to bite the bullet and do a major upgrade. You need to plan a phased budget to reach your final goal.
The first thing I would spend money on is a better GPU. Many games you play may be GPU limited, so a better GPU will give you immediate benefits. The rest of the system may not be able to use it's full capabilities, but you can grow into it. I don't know what your PSU is, but that may need to be upgraded to support the higher power system you will end up with.
Changing motherboard and CPU is a big step because you usually have to replace the Operating System too. If you have an OEM OS it is keyed to your motherboard and may not be transferable (VERY likely)
When you are ready for this upgrade, we can see what the best choice is at that time. It may be an Intel solution.