With that budget you won't get a card that has decent shielding for inside the case.

An external DAC (digital audio converter) is cheaper and doesn't need all that shielding.
This one is affordable and sounds good http://www.amazon.com/gp/product/B00...?ie=UTF8&psc=1

Caveat is if you have shitty headphones or a gaming headset you won't be able to tell. (the tldr is if the brand is marketed a lot like razor, most of the budget is spend on marketing, looks, and bells and whistles not the actual speakers aka gaming headsets have subpar speakers)

and one of the best bang for your buck headphones
http://www.amazon.com/Audio-Technica...audio+technica

If you don't use a deskmic and need a boom
http://www.modmic.com/
Will make your good headphones into a headset and the mic sounds great.

People underestimate how much good sound can change games for the better.