The only change i would do on Steve build is going with AMD Ryzen 7 over Intel i7 6700. Its been proven that for a streaming/rendering/gaming the overall gains are more cores, check the following video for some direct comparisons on a streaming setup,
R7 1700 vs. i7-7700K Game Streaming Benchmarks.
Seems the Ryzen 7 1700 is the best bang for the buck for streamers, up to you if feel the 1800/1800X are worth the extra (i personally i would stick with the 1700), but there are small gains on the others.
The motherboard that i would suggest is one that received perfect scores on
TechPowerUP ASRock X370 Taichi (AMD AM4).
On the CPU cooler for AM4, this is how i see it atm,
Noctua: is the safest as they said free mounts for AM4, and they ship worldwide, as long as you provide a proof of purchase
Thermalright: Seems the newer stock is coming with AM4 in northamerica, the official retailer in the US (nansgaminggear) has posted on amazon questions that he sends for free the kits for AM4 if they don't come inside, but not sure on europe. I seen comments on Thermalright True Spirit 140 Power that already come with AM4 mounts, but you should check with the retailer before buying.
Scythe: Im not too sure on this, as i seen some say they can mount them fine, maybe their mounting bracket allows the position of AM4, but i do expect newer batches to have them on the description. I would check with the retailer before buying.
Coolers that would try to check for AM4 mount for a Ryzen 7 setup,
Thermalright True Spirit 140 Power / Macho RevB / LeGrandMacho / SilverArrow IBE
Noctua: NH-U14S / NH-D15S
Scythe Ninja4 / Mugen5
On the memory, go with memory that has been already tested, usually the QVL List of the motherboard is a good place to start, and then check user that have done builds with them. I seen more so that Gskill Trident seems to be one best supported for people looking to go into 3200. Again this i would chose after the motherboard, as its important to check the memory compatibility, specially in AMD Ryzen.
The other route you could go, is separate boxes for each task, one for gaming and one for capturing/streaming, this ensures that you will have the best experience while gaming but your cost go up as you build 2 PCs, i would do 4 monitor setup, with triple screens for your gaming, and the 4th for remote desktop to the streaming pc / stream monitoring (twitch/youtube chat and console) / temperature monitoring.