I happen to have pretty much the equivalent to your system. Same CPU, same RAM speed, the equivalent GPU power from AMD. 120GB SSD and so on. I play most games on Medium-High.
When it comes to games I'm mostly GPU-bottlenecked (Crysis 3 for instance). GTA V runs smoothly but I'd have to run it again to see exactly how many FPS I'm getting. It was well over 40 anyway, as far as I can remember. The only thing is I'm talking about gaming on three screens at the same time.
Back to your system, I believe CS:GO should run anywhere between 60-70FPS at 1080p on that system, with everything on Ultra.
The bottleneck would be your CPU in that game. So if you would want even more FPS you'd have to go Intel.
A GPU for $50 or less is mostly going to be competing with integrated GPUs, at which point I'm not sure what you're going to use it for but it really doesn't sound like it's worth spending the money on it.
The cheapest I'd get is this or the 750Ti
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127763