IMO it makes more sense to rip and download music than movies. Music is small files that you listen to dozens or hundreds of times, whereas movies are large files that you might only watch once or twice.

labeling and tagging each track, and sorting them into a properly named folder structure

You need to do the same thing for movies and TV shows though.

Lidarr will do this for you, mostly automated.

To rip CDs, I use abcde ("a better CD encoder") on Linux. It automatically tags the tracks based on CDDB or Musicbrainz data.

There's probably a basic app that'll move it to the right directory structure, but I find Lidarr pretty easy to use. I copy the album across to my server, then in Lidarr I add the relevant album then click the button to manually import it, and point it to the right folder. Lidarr will automatically sort it into the right directory structure. I have it configured to use the structure that Plex wants - folders per artist, then folders per album inside those.

That's assuming it has data on Musicbrainz. For MP3/FLAC files from albums that aren't on Musicbrainz, it's a bit trickier. I sometimes use kid3 (KDE audio tagger) as it can pull from other sources like Discogs and Amazon.