Need Streaming Pc

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($99.99 @ Newegg)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($26.98 @ OutletPC)
Motherboard: Gigabyte GA-78LMT-USB3 Micro ATX AM3+ Motherboard ($41.98 @ Newegg)
Memory: G.Skill Sniper 8GB (2 x 4GB) DDR3-1600 Memory ($48.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($48.23 @ Amazon)
Video Card: PowerColor Radeon R9 280X 3GB TurboDuo Video Card ($200.50 @ Newegg)
Case: Thermaltake Commander MS/I Snow Edition (White/Black) ATX Mid Tower Case ($37.99 @ Micro Center)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($58.99 @ SuperBiiz)
Optical Drive: LG GH24NSC0B DVD/CD Writer ($12.99 @ Newegg)
Total: $566.64
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-22 15:39 EDT-0400
 
Solution
Since you have way more money than you need for a streaming system, why not make it small:

I purposely put a overkill PSU just in case in an emergency he needs to use this as a gaming rig.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-4170 3.7GHz Dual-Core Processor ($99.99 @ Micro Center)
Motherboard: ASRock H97M-ITX/AC Mini ITX LGA1150 Motherboard ($89.99 @ SuperBiiz)
Memory: Crucial Ballistix Sport 8GB (2 x 4GB) DDR3-1600 Memory ($50.99 @ Adorama)
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($97.89 @ OutletPC)
Case: Silverstone RVZ01B Mini ITX Desktop Case ($79.99 @ Directron)
Power Supply: Silverstone 500W 80+ Gold Certified Fully-Modular SFX Power Supply ($89.99 @ NCIX US)
Total: $508.84
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-06-22 17:02 EDT-0400