If you go to port 6544 and navigate down the API -> Examples -> HTTP Live Streaming and list either the videos or recordings you get the following transcoding option:
width: auto, 288, 400, 480, 640, 800, 960, 1024, 1280
height: auto, 320, 480, 540, 600, 768, 720
There are also options for audio and video bitrate.
Would these be acceptable? Or is there a resolution that is missing? I figure for Auto I would default to 720p since most phones and tablets should be able to handle that.