If you already have that motherboard, you should be able to run a 6300-series or an 8300-series just fine. Don't expect a very good overclock, though, if any. It's not necessarily that the chipset isn't as good at overclocking as much as it is that 970-chipset motherboards generally don't have OC-friendly power delivery, and with the power-hungry FX chips, a strong power system is a necessity.
Before I switched to Intel, I was using a similar motherboard to the one you asked about. The Gigabyte GA-990FXA-UD3 is a moderately priced motherboard, packed with features (well, as packed as it can be on a several-year-old platform) and a very strong power delivery system. I had my FX-4350 up to 4.8GHz on it for a while (under a Corsair H80i), but the silicon lottery wasn't good to me, and it was only stable at that speed for a few weeks before I started having some stability issues. I backed it down to 4.5GHz and it was just fine, but at that point the overclock didn't do much good. I got to play with an 8350 for a short while and clocked it up to 4.9 in the same motherboard - it was stable, but boy was it hot. (lol)