Don't have H.264 as a video output format option I don't seem to have H.264 as a video output format option. I need it to be able to put out video in RGBA (so with an alpha channel). Tutorials on YouTube all have H.264 available, but not my Blender.

I have Blender version 2.79a
Choose FFmpeg Video and then it's available as codec. In 2.79 the Encoding panel has been improved, see the release notes for more information.