If you can stretch your budget to $135, this card will run circles around those weak GPU's you posted. It's $120 after rebate and you would be able to play most games on high settings.http://www.newegg.com/Product/Product.aspx?Item=N82E16814102908
^Odd, in the list, it says $134.99 and $119.99 after rebate but shows different price in the product page.http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&N=-1&isNodeId=1&Description=HD+6850&x=0&y=0
You will be fine, with low end to mid range cards, your CPU will not be bottlenecked. Also PCI-E generations are all compatible with each other, so a PCI-E 3.0 card will work on a PCI-E 2.0, 1.0 slot and such.
If you cannot go above $100, this card is stronger than both those GPUs too.http://www.newegg.com/Product/Product.aspx?Item=N82E16814134119