"As for other Mac forums, a quick Screwgle search revealed hundreds of them -- none of which I could see as being 100% free of advertisement. "
That's quite true, famous Mac forums such as Apple Discuz, MacRumors, MacNN, also here MacOSX(^-^) ...
Read what is Time Machine from this tutorial, http://www.apple.com/macosx/what-is-macosx/time-machine.html
As to Macintosh recovery programs here are some for your references.
http://www.prosofteng.com/products/data_rescue.php
http://www.macupdate.com/app/mac/36268/data-recovery...