8400 doesn't worth it unless you could buy only intel cpus. 6700 is a great choice but price is still unreasonable. Both 8400 and 6700 can't fit your budget along with motherboard and ram, not mentioning psu, gpu, probably a new case and a cpu cooler. Unless your budget could climb from 500$ to 1500 $. As i said above aim lower. Even an APU i suggested will fit hardly in your budget but it is the most viable choice here.
P.S. If you only intend on gaming at the pc and do nothing else, you might consider buying a console instead.