First bump that budget from 300 to around 800 to 1grand cause getting a computer for 300 dollars you might as well be buying a windows 98 computer honestly it wont run anything period,you wouldnt even be able to play bfh
Ok dude what you need to do is build your pc.
Order the parts and put it together.It'll be cheaper
and better.If you dont know how to put it together there are mass tutorials online.
Get a ATI Raedon 5000 hd series(id suggest the 5570).Then get a 3.2ghz AMD Phenonm processor II(black box edition)4gbs of ram,1tb HDD,64 bit windows 7.Get a ASUS motherboard and or better.If I left anything out or anyone thinks of something better please correct me.