The simplest method seems to be a smartphone to Facebook. From there it can get as complicated and as advanced as you want. I would stay away from GoPro for streaming; the streaming view is fixed to a wide view. Streaming with any device to YouTube requires at least 1000 followers. There is a way around it, but is, again, complicated.
Here is a video we put together for many of the options available, with regard to hardware:
Facebook page via Smartphone works fairly well as long as you have a good internet signal.
A little tip: If you make the Facebook page public, people can watch the video without a Facebook account (at least on a computer; haven't tried it on mobile). Just go to the direct link (facebook.com/yourpagename).