Mobile Twitch live streaming question

I want to live stream to twitch+youtube (preferably at the same time, if not one would do) from a mobile device for social / outdoor activities. I'm stumped when it comes to what would be the best setup or electronic device for streaming. I'm looking for

1. Video stabilization (because im going to have the camera on me and moving around
2. Frame rate
3. camera quality since two phones/cameras can shoot in 1080p but one can be sharper, better colors, record better in dim lit areas or night time. Resolution isn't that big a deal to me overall minimum 720p
4. Price

I'm leaning towards a all in one up to date smart phone but no idea which one i should get. Is it worth it to go with something like a GoPro, I feel as though I'm strapping on an extra device that has to be connected to my smartphone anyway so wouldn't make more sense to cut out the middle man and use your phone with decent camera anyway? Their is also this company called Livestream broadcaster but their products are pretty expensive but new android smartphones can range from 500-800 $ as well.

What to do.