By commandline, with recent versions, it should work with your command options and the name of the directory(ies) instead of the files:
vlc --LZ "Party Music"
If your path includes spaces you need to include it between
Only if you modified the default options you may need to add also
--playlist-tree only shows the playlist as a tree. Enable if you want.
If you are not in the parent directory of
"Party Music" you have to specify the whole path, complinat with your operating system (e.g.
"C:\Music\Party Music" or
"~/Music/All Music/Party Music" or
VLC usually remembers the last setting you decided. If you run from commandline (or with a link built for this purpose) it will overcome the usual behaviour following the prescription specified by the options without changing it. If instead you will change some setting during its run it will remember the next time.
-L, --loop, --no-loop Repeat all (default disabled)
-Z, --random, --no-random Play files randomly forever (default disabled)
VLC will randomly play files in the playlist
until interrupted. (default disabled)
Auto start (default enabled)
Display playlist tree (default disabled)
Tested on VLC media player 2.1.6 Rincewind on Ubuntu, but it should work on precedent versions and for different operating systems too.