Need help with a good GPU

Hello there! I have finished the main part to my pc and am looking to add a GPU to it now. (Let me know if i left anything out)

Here is my build: http://pcpartpicker.com/user/HelloImTinyT/saved/1uKt  

So, all i need is some suggestions on what GPU would be good. I am trying to keep the price under $100 but by all means be cheaper than that. 

Another quick question and sorry if its a dumb one. With this build would it be possible to play games such as BF3, Crysis 3, or maybe even Skyrim? Just wondering, I know running Skyrim is a long shot but just in case :)

Anyways Thank you for your help and have a great day!

7770, or, if you can spring it,a 7790. For that budget, you will be able to run those games at low-medium settings, as long as you're not at a high resolution. For 1080p, it will be fine, though. I'm guessing you don't have a 1440p monitor, anyway ;)

Um, the most graphically intensive game you mentioned was chrysis 3, which your build would have a hard time handling. I'd really recommend a 7790. What's your resolution?

1920x1080 

Alright thank you!

Okay, yeah. Really try to shoot for the 7790, AT LEAST. I'd really try to get a 7850 or even a 7870 xt, but that's twice your budget.