I like ATI, but I cannot comment as much on their cards as I've not owned one in a while. Personally, if I had the money to spend, this is what I'd be tempted to get.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127565R
For the money, that's usually a 200+ dollar card. I put a GTX 570 in a guy's system, and it was smooth. According to what I read, there were only a few frames per second difference with the 560 vs the 570.
If you are dead set to go ATI, this card seems to be top of the line for under 200 on newegg.
But according to this thread, the 560ti is a better/faster card
http://www.tomshardware.com/forum/316895-33-galaxy-evga-radeon-6870
Since you say it's the first time you've picked one out, you may need a power supply upgrade. If so, might I suggest this instead?
The Nvidia GTX 460 768 mb.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130570
Keep in mind, this is last years card, but does support dx11 and newer features. It's 169.99, but comes to 129.99 after a rebate. There is a cheaper ASUS card on there, so take a chance if you want, but EVGA is good, and some people with ASUS seemed to be having trouble getting their rebates.
The 460 is NOT going to be as good as say a 560, but it is a good card for what you pay. According to some places, it performs a little better than a 5830.
Also, I would look at a newer power supply.
Most guys would not recommend this, but kinda liking this Rosewill power supply.
http://www.newegg.com/Product/Product.aspx?Item=N82E16817182199
Price is 50 bucks and it has 41 amps on it, and it 80+ certified, so it should be decent for that price.
Facebook
Twitter
Instagram