If you're using J. River Media Jukebox for playback you'll probably find it more convenient to use J. River Media Jukebox for tagging changes and filename changes as well. JRMJ has some good tagging and renaming tools built in (Tools >> Library Tools >> Rename, Move & Copy Files...) as well as the tag panel.
JRMJ uses a database as well as the tags in the files to organize. When using a media player that combines a database it us usually best to do tagging and filename changes within the media player so the database stays current and in sync. You can make tagging changes outside of the media player, but you should be smart about it. If you want to make changes outside of JRMJ then make sure JRMJ is configured to "update for external changes" and "fix broken links" (Tools >> Options >> Library & Folders). JRMJ will get the database back in sync as best it can after external changes.
The most important tags (as named in JRMJ) are ALBUM, ARTIST, NAME, and ALBUM ARTIST if you like special names for multiple artist albums.
GENRE is handy for organization, but not critical, and it's up to you as to how detailed you want to make the genre.
TRACK # is important as well for complete albums. JRMJ uses the track number to help determine if an album is complete or not and to help group multiple artist albums. I'm not sure what JRMJ would do if you deleted the TRACK # tag from all files. Would it still correctly group files together as albums?
If you have complete albums that come on 2 or more CDs it is helpful to have the DISC # tag correctly set. You can use DISC # as part of your naming scheme.
JRMJ assumes that the files for each album are in individual directories. So your file naming scheme and directory structure needs to put each album in an individual directory.
Once you have all of your files correctly tagged it is easy to redo the entire directory structure and file naming structure (Tools >> Library Tools >> Rename, Move & Copy Files...). You can rename and move based on tags and even scripting functions.