You need to choose a codec that can include an alpha channel. Here's relevant information from After Effects Help:
"Many file formats can include an alpha channel, including Adobe Photoshop, ElectricImage, FLV, TGA, TIFF, EPS, PDF, and Adobe Illustrator. AVI and QuickTime (saved at a bit depth of Millions Of Colors+), also can contain alpha channels, depending upon the codec (encoder) used to generate the images stored in these containers. For Adobe Illustrator EPS and PDF files, After Effects automatically converts empty areas to an alpha channel.
When specifying the color depth for an output image, the plus sign (as in Millions Of Colors+) denotes an alpha channel. Similarly, choosing to output to 32 bits per pixel implies an output depth of 8 bits per channel for each of four channels: RGBA."
Your list of resources is phenomenal, and actually I'm working with the Classroiom In A Book. As an experienced PrPro user, I'm already familiar with alpha channels, layers, etc. I'm just not understanding how to "get rid of" the black background in my composition, leaving the logo and line of text. Perhaps my confusion stems from the background not appearing as an actual layer anywhere that I can find, i.e on the timeline, etc. so I can specify that it should be transparent. Perhaps I'm not exporting properly? I'm going to Make Movie to render on output as an .avi for use in PrPro. Is that not correct?
Well, as is often the case, a new day and a fresh look at things often reveals the answer. In this case I simply had to specify RGBA in the output channels for .avi. The default is RGB. Anyway, I changed it to RGBA (which exports the alpha channel) and viola'!It's always something simple, isn't it? Many thanks!