Live stream from GoPro to YouTube or another video service Here is what I would like to do.

Get the cheapest GoPro camera(s) that will live stream events to YouTube without any other equipment. I would like to record the event to YouTube as it is happening.

The bandwidth is not great but I do not care about the quality of the livestream. I'm more concerned about highest quality video recording.

Here are my questions:
1) Which GoPro camera is appropriate for this job?
2) Is it possible to select some stream settings that will sacrifice the quality of the live stream for better quality recording?

Thanks..
No GoPro is appropriate for the job by itself.  Any of them (or even a basic webcam) could work as a camera, your problem is that you need something that can encode and send a stream by itself.  That is a specialized device and not something a GoPro can do.  You would want a either a device built for doing a direct stream (such as an IP camera) or you would want to have a camera with a clean HDMI (or other) output that can be fed in to a stand alone streaming device.

For the second half, recording quality and stream quality are completely and 100% independent of each other.  They are both two different captures of the same visual information, but the sensor is going to pick up maximum quality regardless of if you are recording in some low bandwidth format or not and the steam is going to run off the output which should be the high quality format regardless of what quality you are streaming at.