Best graphic card on the cheap

I am just looking to get the best graphics card for as cheap as possible. $100 is the absolute most I can afford, but the cheaper the better (and note I don't care if I have to replace it in a year, I will have more money in a year to do that with, just in a tough spot right now). Really there are 2 games right now (Bioshock Infinite and Borderlands 2) that I can't play and really want to play, and a few others that I struggle to run but can do so on really low settings. I believe I just have integrated graphics from 3 or 4 years ago, so really anything is an upgrade (I am sort of amazed that integrated graphics have gotten me this far). So any suggestions will be cool. Thanks :)

@endersdragon:

R7 250

or

GTX 650

Thanks, any good cheaper ideas (I know I said $100..., but cheaper really is better) :)

$74.99 w/ rebate - PowerColor Radeon HD 7770 GHz Edition

$89.99 w/ rebate - MSI GeForce GTX 650 Ti

Yeah, these for sure. I myself was going to recommend the 7770.

If you can use ebay this is a great deal, but first what is your power supply at least a wattage and do you know if you have pcie cables and a slot on your mobo. If not what is your current GPU?

$100

http://www.ebay.com/itm/HIS-AMD-Radeon-HD-6870-H687F1G2M-1-GB-GDDR5-SDRAM-PCI-Express-x16-Graphic-Card-/200978126794?pt=PCC_Video_TV_Cards&hash=item2ecb3ad7ca

or search for hd 6850 all are only under $80

also I believe the gtx 460 (only get the 1GB version) is around $80 also.

Be careful of wattage, you have to look what your power supply can handle, and also make sure you have the proper PCIE slot for it.

As far as cheap cards, the above are good suggestions.

People change vid cards like underwear, look for used ones on e-bay.

One of my pcs has a 7770 and it handles anything. I have a post looking to upgrade cpu and ram. I think this card will work with futurw games until a point as well