Thoughts on this system for streaming/gaming

Many problems:

Crap PSU
Bottom end GPU
Wasting money on CPU
Small HDD
Single channel RAM

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($133.79 @ Amazon)
Motherboard: Gigabyte GA-970A-D3 ATX AM3+ Motherboard ($83.98 @ Newegg)
Memory: G.Skill Sniper 8GB (2 x 4GB) DDR3-1600 Memory ($43.98 @ Outlet PC)
Storage: Seagate Barracuda 500GB 3.5" 7200RPM Internal Hard Drive ($59.13 @ Amazon)
Video Card: HIS Radeon HD 7870 2GB Video Card ($209.99 @ Newegg)
Case: NZXT Gamma Classic (Black) ATX Mid Tower Case ($34.21 @ Amazon)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($54.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Total: $710.05
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-02-20 00:47 EST-0500)

This will game about 4x as well.

Use an AMD FX 8350 , 990FX motherboard and 8 gigs of RAM

http://www.youtube.com/watch?v=eu8Sekdb-IE&list=UUNovoA...

Use a graphics card powerful enough to run the game well . Start at the 7850 and work your way up from there

and never ever ever buy a coolmax psu
80 + bronze or better rated units from reputable manufacturers only

The gamma is a dreadful case too . Only buy it if you have a sense of humor

Looks as though you're on a budget with the listed parts. First off you'll want to spend less on the CPU as all your other parts will bottleneck. If you're going with Micro ATX, I'd suggest going with a mATX case as they usually come with a PSU too. Your PSU is made by a company I am not familiar with so you may want to stay away from it and stick to SeaSonic, Corsair, or an reputable name. The CPU cooler will come with thermal paste so you shouldn't have to worry about buying any. What's your budget? I'll put something together that is around the price range your build is. http://pcpartpicker.com/p/EHro

NEVER use a psu that comes with a case. Common knowledge.

Take a look as the build I posted. It will be considerably better than this one.