I'm working on my very first joomla (3.2) site.

Your ALLVIDEOS plugin looks like it might be perfect for me. I installed the module using extension manager, then "enabled" it (the doc talked about "publishing" it).

I've managed to discover the tags and can have the viewer show up in an article and that's good), but I was hoping to have the video show up in a module, or at least not encapsulated within an article -- a permanent video in a permanent place on the home page.

You can use it in a custom HTML module. All you have to do is enable the option Prepare Content in the module's settings.