For gaming+ streaming the fx 8350 is perfect.
I5-3570k and fx8350 are pretty much similar in overall performance.
In games the i5-3570k is mostly a bit ahead(also depend on games in which the fx 8350 is better), while the fx8350 is better in streaming and tasks which benefit from the use of more then 4 cores.
Both cpu's are great,
Fx 6300 is the best bang for the buck..., when overclocked it can compete with fx 8350...
For ~250$ range the sapphire hd 7870 XT is the best choise
http://pcpartpicker.com/part/sapphire-video-card-111992020g