I have 8gb ram and a amd-10 6800k processor, i was looking for an amd GPU that could run the game on high with these specs (cheapest as possible).
high settings amd GPU
280x is highly playable on high settings, better to run low though imo, looks prettier and more fps!
@SiegeFace he said the 280 was too expensive, pretty sure the 280x will also be too expensive 
To the op, try and get a nice second hand videocard or grab an nvidia 750 ti
So maybe the OP could tell me/us his budget and we can figure something out for him.
My advice though on that APU/CPU you have there, not a good choice imo, I had an a6-3670k (although a amazing processor/apu for the price £30) it could “bottleneck” a potato, so any mid-high range gpu is going to suffer due to the apu you have, just be prepared for that instance…
Tell me your budget, and I can figure something out.
EDIT: Might be worth going secondhand, its a risky one but could net you a good deal.
Unreal Engine 3, what Dirty Bomb uses, is famous for not really caring what kind of a GPU you have for most things and is typically limited by your CPU. I have no clue how powerful your CPU is but if it’s one of the medium to lower end ones you might run into some issues depending on what kind of performance you’re wanting/expecting.
Basically, don’t spend a lot of money on a GPU for Dirty Bomb if that is mainly what you care about playing.
It’s very hard to tell my budget as i live in argentina and prices here are very different. Two gpu that cost the same in united states may have a huge price difference.