Do you think this build will work well for Rendering Video, Gaming, and Streaming

Solution
Its a good build for those things, but with some changes you can get more for the same price:
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i7-6700 3.4GHz Quad-Core Processor ($295.52 @ B&H)
Motherboard: ASRock H170A-X1 ATX LGA1151 Motherboard ($76.98 @ Newegg)
Memory: Crucial 32GB (2 x 16GB) DDR4-2133 Memory ($111.99 @ Newegg)
Storage: Crucial MX300 525GB 2.5" Solid State Drive ($128.99 @ SuperBiiz)
Storage: Hitachi 2TB 3.5" 7200RPM Internal Hard Drive ($53.00 @ Amazon)
Video Card: EVGA GeForce GTX 1060 6GB GAMING Video Card ($249.99 @ SuperBiiz)
Case: Deepcool TESSERACT SW ATX Mid Tower...

king3pj

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It looks pretty well balanced to me. The i7 will be good for rendering and streaming and the 1060 is a great choice for 1080p gaming.
 
Its a good build for those things, but with some changes you can get more for the same price:
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i7-6700 3.4GHz Quad-Core Processor ($295.52 @ B&H)
Motherboard: ASRock H170A-X1 ATX LGA1151 Motherboard ($76.98 @ Newegg)
Memory: Crucial 32GB (2 x 16GB) DDR4-2133 Memory ($111.99 @ Newegg)
Storage: Crucial MX300 525GB 2.5" Solid State Drive ($128.99 @ SuperBiiz)
Storage: Hitachi 2TB 3.5" 7200RPM Internal Hard Drive ($53.00 @ Amazon)
Video Card: EVGA GeForce GTX 1060 6GB GAMING Video Card ($249.99 @ SuperBiiz)
Case: Deepcool TESSERACT SW ATX Mid Tower Case ($39.99 @ SuperBiiz)
Power Supply: Rosewill 550W 80+ Gold Certified Semi-Modular ATX Power Supply ($64.99 @ Newegg)
Total: $1021.45
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-08-25 10:12 EDT-0400

Your build is allows for overclocking, though if you get a non-overclocking build you will still have more than enough performance for your needs. It also allows to solve the problem with your build, a too small SSD and more ram.
 
Solution