Upgrade for streaming advice

Hello, I am looking for an upgrade to my current system in order to have a better streaming quality.

Current pc:   http://pcpartpicker.com/p/4Wp9RB

Note: I also have a dvd-rw drive and the ram isn't specifically that type, I don't know which it is, but it is 2 x 4gb DDR3 1333mhz ram (the processor required 1333).

 

I have around $350.00 to spend on new parts, I know that I'll need a new processor because the current one can't handle streaming. Looking to stream CS:GO and possible future games.

I am open to going with a new motherboard and cpu combo if it is within that price range. (Not a brand loyalty kinda guy.)

 

p.s. I'm willing to go to $400 IF it is a significant boost compared to something lower price. 

second p.s. Internet and settings are not a problem. Most likely going to use OBS unless you can persuade me.

Extra info: Florida, USA; Have amazon prime if it matters; I'm willing to overclock within reason; No peripherals needed (ATH-M50s, Blue yeti snowblall, death adder 2013, logitech G710+)  

 

 

Instead of upgrading, try using AMD's Game DVR through raptr.  I use it for recording and it's great for the most part.

http://raptr.com/

Setup can be interesting, but just make sure the in game interface is on and that your streaming hotkey and option is turned on.

This is basically AMD's version of NVIDIA's shadowplay.