Well we kinda already made builds for you in another thread.
http://pcpartpicker.com/list/mtbbjcIf you really can't push it to over 600$, I guess you can get a 950 or r7 370. But wouldn't recommend it because you gonna play BO3
But this system will already meet its limit in today's games.
I would recommend you saving up a bit more to get a i5 6400/6500 plus gtx 970/1070 or RX 480
get a 20-29$ key here. depending on what version you like
http://www.kinguin.net/catalogsearch/result/index/?q=windows