A cheap PC with dedicated GPU for Battlefield 3&4. Hopefully around $450. Thanks!
What resolution?
Do you need a mouse/keyboard/audio set up?
Do you have an older PC lying around you can cannibalize for some parts namely a hard drive/RAM/case?
if you want all new parts here
http://pcpartpicker.com/p/Mqc8qs
otherwise I suggest the craigslist route
You can start out with this build: http://www.reddit.com/r/PCMasterRace/wiki/builds#wiki_the_next-gen_crusher
And then tweak the details.