What GPU do I need to stream?

[Lucid Legacy]

PCPartPicker part list: http://pcpartpicker.com/list/H3TRkT
Price breakdown by merchant: http://pcpartpicker.com/list/H3TRkT/by_merchant/

CPU: Intel Core i5-6500 3.2GHz Quad-Core Processor ($199.99 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.38 @ OutletPC)
Motherboard: Gigabyte GA-H170-GAMING 3 ATX LGA1151 Motherboard ($77.98 @ Newegg)
Memory: Crucial Ballistix Sport LT 16GB (2 x 8GB) DDR4-2400 Memory ($64.99 @ Adorama)
Storage: PNY CS1311 120GB 2.5" Solid State Drive ($39.99 @ Best Buy)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($48.49 @ OutletPC)
Video Card: EVGA GeForce GTX 970 4GB Video Card ($229.99 @ Newegg)
Case: Rosewill BlackHawk ATX Mid Tower Case ($59.99 @ Newegg)
Power Supply: Cooler Master 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($69.99 @ Newegg)
Total: $791.79
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-07-31 15:16 EDT-0400

I am looking to build a pc for league and streaming as it has always been something I've wanted to try. I believe the i5-6500 would be the best value for my CPU. The RAM and SSD are completely adequate for streaming. But as far as the GPU goes, I am unsure if I should buy the GTX 970 or the R9 380x. Or maybe I don't need all of that and I can downgrade to the much cheaper GTX 960. But if I downgrade I don't want to bottleneck the entire pc. Any help and suggestions for what I need to do so I can play league on high settings and stream smoothly are highly appreciated.

 

[TerryLaze]

LoL is quite undemanding,any nvidia card (from the 650 onwards) can use shadowplay to stream without any effect on the CPU,if your internet upload speed is not that good you can use the intel's iGPU by using OBS with quicksync(QSV) it has the best available ratio between quality and size next to using the CPU cores, wich you would be able to do as well without any problems if you want to.
Celly with 650 can play LoL and stream at 1080/60FPS highest settings and get ~100FPS
[video="https://www.youtube.com/watch?v=-wek5XoyRRU"][/video]

 

[Lucid Legacy]

LoL is quite undemanding,any nvidia card (from the 650 onwards) can use shadowplay to stream without any effect on the CPU,if your internet upload speed is not that good you can use the intel's iGPU by using OBS with quicksync(QSV) it has the best available ratio between quality and size next to using the CPU cores, wich you would be able to do as well without any problems if you want to.
Celly with 650 can play LoL and stream at 1080/60FPS highest settings and get ~100FPS
[video="https://www.youtube.com/watch?v=-wek5XoyRRU"][/video]

So the GTX 960 would be as good as I need for what I hope to do? How is the rest of the build from your perspective? This will be my first build and I don't want to make a costly mistake.