Twitch streaming from Big Picture using Steam Link - what're my best options?

[Nostalginaut]

I've only ever really streamed on Twitch briefly from a PS4. I have Twitch Studio on my PC and confirmed that it "works" but didn't really bother playing anything for more than a couple minutes with it.

I'm hoping to do some streaming soon to raise money through Extra Life, but a lot of the gaming I seem to do is through my Steam Link in another room, which uses Steam Big Picture.

Will Twitch still work with this? What about audio streaming - is there any kind of remote microphone I can hook up to my xBox controller or the Steam Link itself that would work?