Which Ryzen should I use for console streaming to twitch?

Most [however not all] ryzen processors do not have onchip video so you would need to install your video card.
I do not stream anything however I can give you some insight into ryzen. I have two personal systems; an intel 7600k overclocked to 4.5gig and a ryzen 1700X overclocked to 3.9gig. Both work well and on a single core benchmark, the intel has a slight advantage [not surprising since it is clocked quite a bit higher] The difference comes on a multi core benchmark; the ryzen system blows the intel out of the water; doubling the cinebench cpu score. On realbench, the ryzen system outscores the intel by 35%

The only problem is that with an intel, you can just slap parts together and it works; not so much with ryzen. To achieve the level of performance indicated above, requires careful tuning in the bios. CPU multi, blck, ram speed, ram timings, and ram voltage must be set manually in the bios. In short if you are the type of guy who likes to work on things, go ryzen. If you just want to put parts together and have it work, go intel.

 

Any motherboard that supports ryzen processors and has a pci-e 16 slot should work. The 10xx cards need a uefi type bios and any board that supports ryzen will have a uefi bios.