Switching from console to pc?

So iv looked at the forum posts and there were some that helped but i still need some questions answered. 1) im selling my xboxone so i will have a budget of $625. i only want tp spend 200-250$ on the cpu i dont care if it is intel or amd. i need help on what cpu to get i looked at some forum post and saw the fx-8350 or the amd x4-750k open to other suggestions. well i have one concern that is i stream to twitch often and need cpu guts to run various programs OBS, Xsplit, Evolve will the cpu's have the power to run them?

 

games i will be playing - arma 2,arma 3,rust,bf4 and The division 

 

RANT TIME!!!!!!!!!!!!

My xboxone is the biggest peace of shit i have ever owned. I bought it because i play Forza 5 (its a racing game) i also im a really big bf4 player im ranked 91 in the world. well my bf4 crashes all the time my forza i can only play by my self online dose not work for me and trust me iv tried everything to fix it. and most of all if you are playing a game and you zoom out to navigate the dash board it is MIND BLOWINGLY SLOOOWWW! So recommendation is stay far away from it. 

 

Now please PC universe help me and welcome me with open arms!

The 625 budget is not all cpu it for a case,ram,cpu and power supply.

This should work out for you and is a little below budget: http://pcpartpicker.com/p/3e8n0

If you live by a micro center you could potentially save more by walking in. :D

It would be nicer if you had a larger budget, but here's what I came up with.

http://pcpartpicker.com/p/3eaSJ

This would give you worse gameplay frame rate, but would be less cpu bound for streaming:

http://pcpartpicker.com/p/3eaCF

And yes, Forza 5 looks like crap on the Xbox One.