is the AMD FX-8320 BLACK EDITION a good gaming processor??

I would not recommend an upgrade to an FX 8320 on your current motherboard. Your motherboard lacks the required cooling and only has 4+1 power phase. At most you could probably run the FX 8320E or FX 8370E, both are fine processors and at 95W will do much better with your motherboard than a 125W 8 core. With 4+1 power phase your not going to be able to get much of an overclock out of even a 8320E or 8370E, probably be able to overclock to the turbo core settings at best as your motherboard lacks the required cooling and only has 4+1 power phase.

If you are just trying to do an upgrade to keep you going for a couple years before doing a major upgrade then I would suggest either the FX 6350 (which should be able to overclock on your board) or a FX 8320E or FX 8370E and at most get maybe ~4.3Ghz out of it. A rig with the GTX 960 and FX 8370E @ 4.3Ghz should keep you gaming on high settings for the next couple of years (your probably not going to be doing Ultra @ 1080p, but can have a really good gaming experience on med - high settings @ 1080p). If you could squeeze another couple years out of your rig before upgrading there should be more of a selection in the "high end" CPU market with Zen releasing end of this year / beginning of next so instead of having only Intel to choose from in the high end market there will be Zen or Intel which should hopefully translate into better prices when you go to do a big upgrade - new DDR4 motherboard, processor, GPU, ect....

If you want the best gaming solution right now (1080p all Ultra settings in games) then you will need to upgrade to Intel now, and should be looking at Skylake. The "cheapest" upgrade would be to go to an i3 6100 which would require a new motherboard, new DDR4 Ram, and the processor. Even then in some games your GTX 960 is going to limit you to high settings and not Ultra @ 1080p. If you upgrade to Skylake now you have the option of upgrading the processor to Kaby lake in a year or two, so that motherboard would have an upgrade path.

So if you want a solution that will keep you gaming at high levels for the next couple of years your looking at getting a FX 6350 (and overclock it) or FX 8320E / FX 8370E (with a mild overclock). If you want the best possible upgrade right now you have to switch to Skylake and get new motherboard, DDR4 RAM, and processor but would then have an upgrade path though Kaby Lake.