the 2600 is a much better deal than the X. Right now it's a 40-50$ price difference and when it comes to gaming the 2 pretty much perform the same. The x is a little faster, but you could buy a really nice cooler for 50-60$ and then overclock it a little. I think the retail was normally only 20$ difference or something, but right now non x has been on sale selling for 160 and x is 200+. If you are looking for a good cooler, I would recommend this one below. Purchased 2600 recently and during very heavy stress testing the cpu has yet to even hit 60c. You can buy a cheaper second 120mm fan to put on the backside of this. I bought a Thermaltake Riing 12 for 7$ to put on the back, works great.
https://www.amazon.com/Noctua-NH-U12S-SE-AM4-premium-grade-cooler/dp/B01N9X2YYN/ref=sr_1_1_sspa?s=electronics&ie=UTF8&qid=1538415727&sr=1-1-spons&keywords=noctua+nh-u12s+amd&psc=1
Here is a good review with a lot of benchmarks.
https://www.pcgamesn.com/amd-ryzen-5-2600-review-benchmarks
The only issue I see is trying to get 120fps in some of these games while also streaming. Doesn't matter if you have an i7 8700k w/o a GTX 1080/ti 120fps is not going to happen.
https://www.techspot.com/article/1532-pubg-cpu-benchmarks/
GTX 1070 and 120fps 1080p is going to struggle a bit on many AAA games.
https://www.gamespot.com/articles/nvidia-geforce-gtx-1070-review/1100-6440307/
If you can't hit 120fps 1080p then 1440p is definitely not happening. Now games like overwatch, fortnite, etc.. yeah, that will run fine, but these are the games that really don't look much better even at a higher resolution. If you want to tweak the settings a bit and adjust the framerate then your fine. If you are someone who is dead set on ultra preset (i haven't ran preset in ages) and won't turn shadows down from ultra to very high in order to gain 20fps because they think they can actually notice this during real gameplay, then save up and buy a GTX 1080 and i7. With minor tweaking, you can reach the sweet spot where you literally can not tell the difference visually while playing, but you can gain a huge boost in your fps.
I would definitely not go with a GTX 1060 for what you want. The 1060 is the perfect card to do 60-90fps 1080p ultra or 1440p 60ish fps tweaked settings. Now if you want to stream in 1080p 60fps (custom settings) and then stream 720p 30fps the 1060 and ryzen 2600 should get the job done just fine. That would be on the more visually appealing games. If you play mostly stuff like fortnite and less pubg then a 1060 definitely will be fine.
What are your future plans? When do you plan to upgrade your display? Pricing is slowly getting back to where it should be. The 1070s seem a bit high still, but the 1060 and RX580 has dropped a bit and they have some killer deals on the 580 which is basically same as a 1060.
https://www.newegg.com/Product/Product.aspx?Item=N82E16814125962&cm_re=rx580-_-14-125-962-_-Product
Another option could be buy a good cpu now, save 200$ on your GPU with something like this. Use a RX580 until you are going to upgrade your display. Do you have a 120hz display right now? Then purchase the 1070 equivalent when you upgrade the display and make a few bucks selling the old gpu. This could be a good option because of how much of a jump they have been making the last few years on each new gpu model.
Compare a gtx760 to a 950, 950 cost less and outperforms. then the 960 to the 1050ti, again cost less and outperforms. the 1060 outperforms the much more expensive 970. The R9 270x cost about the same as a RX 480, but the 480 greatly outperforms the 270x. The 270x could not run 60fps+ ultra in basically every AAA game and the 480 can, but yet the cost the same amount. If they keep on this pattern, the next model to come out equal to the previous 1070 in the sub 400 price range could be better performing than a current 1080/ti.. This also assumes pricing doesn't get royally fd again. I have a feeling it won't because now you basically need expensive mining setups and gpu is not the way to go.
good luck