That's an FM2+ motherboard, and so is the CPU, so they'll work together. It's a micro ATX motherboard so it'll fit in any case that accepts micro ATX motherboards. Sony Vegas Pro 11 uses Opencl for hardware acceleration, so you can choose from AMD or Nvidia. The A10-7860k is not a CPU, it's an APU. It incorporates graphics onboard. Because of this, APUs aren't as fast as CPUs in demanding tasks like video editing. You are on a tight budget, you might consider using the onboard graphics and not buying a videocard yet. Combat Arms does not look demanding, the onboard graphics are probably enough for it.
I would not advise buying an R7 250, it's not powerful enough to be worth buying if you have A10-7860 onboard graphics. An RX 560 or GTX 1050 are the minimums you should look at if you really want a videocard.