To stream you will require more than 4 threads so best choice here for a budget CPU is the Ryzen 5 1400, decent little gamer with 4 cores and 8 threads. This build does not include Operating System (OS) software, keyboard/mouse, monitor and a Wifi card/stick if it is needed.
PCPartPicker part list:
https://pcpartpicker.com/list/pd9bgL
Price breakdown by merchant: https://pcpartpicker.com/list/pd9bgL/by_merchant/
CPU: AMD - Ryzen 5 1400 3.2GHz Quad-Core Processor ($157.49 @ SuperBiiz)
Thermal Compound: ARCTIC - MX4 4g Thermal Paste ($5.49 @ OutletPC)
Motherboard: Gigabyte - GA-AB350M-D3H Micro ATX AM4 Motherboard ($84.33 @ OutletPC)
Memory: Team - Elite Plus 8GB (2 x 4GB) DDR4-2400 Memory ($62.99 @ Newegg)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive ($49.88 @ OutletPC)
Video Card: Zotac - GeForce GTX 1050 Ti 4GB OC Edition Video Card ($143.77 @ Amazon)
Case: Zalman - T2 Plus MicroATX Mini Tower Case ($33.99 @ SuperBiiz)
Power Supply: EVGA - 450W 80+ Bronze Certified ATX Power Supply ($34.99 @ Amazon)
Total: $572.93
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-07-16 11:00 EDT-0400