For streaming you will need enough cores/thread to manage both processes in real time, the minimum I suggest is 4c/8t. Here I chose the Ryzen 1600X with 6c/12t so that you could assign 2 cores to hardware encoding taking some of the load off the GPU. You will still have 4c/8t to game. 16GB of RAM will be needed. I tried to fit an SSD into the build but hit your upper budget limit. No way I could fit a GTX 1070 into the build, had to go with the cheapest 1060-6GB I could find.
1600X Build
PCPartPicker part list:
https://au.pcpartpicker.com/list/2KTXQV
Price breakdown by merchant: https://au.pcpartpicker.com/list/2KTXQV/by_merchant/
CPU: AMD - Ryzen 5 1600X 3.6GHz 6-Core Processor ($328.00 @ Shopping Express)
CPU Cooler: Cooler Master - Hyper 212 LED Turbo (Red) 66.3 CFM CPU Cooler ($49.00 @ Umart)
Motherboard: ASRock - Fatal1ty AB350 Gaming K4 ATX AM4 Motherboard ($139.00 @ Shopping Express)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-2666 Memory ($193.82 @ Skycomp Technology)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive ($64.00 @ Shopping Express)
Video Card: MSI - GeForce GTX 1060 6GB 6GB Video Card ($359.70 @ Newegg Australia)
Case: Corsair - 200R ATX Mid Tower Case ($81.00 @ Shopping Express)
Power Supply: EVGA - 500W 80+ Bronze Certified ATX Power Supply ($78.46 @ Kogan)
Total: $1292.98
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-07-17 23:43 AEST+1000
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