Well, with particpicker, you're getting the cheapest prices. They collate all the pieces and send them to you. Its not much different from your original site, only they will charge a margin to earn some extra dollars
Yes, for both high gaming FPS AND high quality streaming, more cores/threads wins here. That article i posted above will explain it in fine detail, and with some solid recommendations. So any of 1700x/1800x/2700x/I7 8700k, will be monsters at doing that.
Comparing the 8600k to my 1600x for examplle (this is mostly based on similar price for CPU). The 8600k games like a champ, but include high quality streaming at it just runs out of resources. The extra 6 threads on the R1600x makes up for that, and has nearly flawless video output.
For mainstream CPU's that we're talking about, Intel will always win out on pure FPS. Factor in streaming, multitasking, and high resolution gaming, and it balances out much more.
So for performance per dollar I'd go with Ryzen, and for pure performance I'd go with Intel. I've had both, and have always been happy with my purchases.
With all of that said, I think you're on the right track. I'd be looking at a 1600x or above from AMD, and an 8600k and above from Intel. Depending exactly what you want to achieve, you can tailor the build to give you longevity (but not future proof

)
Either way, for mainstream gaming, at 1080p 75hz, both an 8400/8600k or a 1600x would be absolutely a perfect match with the 1070ti.
Ryzen will be a cheaper build right now.
Don't worry about over asking anything. That what this community is about. Trying to depart knowledge. I'm still learning all the time, thanks to Tom's forum members, and believe me, I STILL ask lots of questions