Ooh awesome ask! The musicals you want to watch are the Kaguya ones, the Dracul Series and even though its more of a celebration, it does have an original story: The 10th Anniversary Festival - Sanctuary of Love (Ai no Sanctuary).  Also, in my opinion, the runners up of having an “originalish” storyline would be the two SuperS musicals and The Eternal Legend (Eien Densetsu). While those shows do cover certain arcs, the musicals add enough of their own twists and changes to the story that they practically become an original telling of those arcs on their own.

I’ll break it down the Kaguya and Dracul Series with a tiny synopsis!

First up are the Kaguyas:

• 1999 Spring - The Legend of Kaguya Island (Kaguya Shima Densetsu)
• 1999 Summer – The Legend of Kaguya Island (Revised Edition) - Summer Vacation! The Jewel Expedition Party (Kaguya Shima Densetsu (Kaiteiban) - Natsuyasumi! Houseki Tankenta)
• 2004 Summer - The New Legend of Kaguya Island (Shin Kaguya Shima Densetsu)
• 2005 Winter - The New Legend of Kaguya Island (Revised Edition) - Marinamoon Final (Shin Kaguya Shima Densetsu (Kaiteiban) - Marinamoon Final)

The story between the original Kaguya Island and the “new” Kaguya Island musicals are similar but they have some differences in plot, a few characters and music. I highly recommend watching both and taking from either or as I find each version adds something to the overall story. Kaguya’s story, to simply put it, is about the Usagi and co. getting stuck on an island while being pursued by Loof Merrow and her band of Pirates looking for the Silver Crystal and a new enemy, Dark Plasman, the personification of a comet who wishes to take the place of Earth. The revised version of the original musicals offers a fun scene of Neo Queen Serenity, King Endymion and Chibiusa in Crystal Tokyo that is worth seeing. :D

Second, is the Dracul Series. We highly recommend that these musicals be watch in order as they are the only ones that actually have some semblance of a continuity (all the other shows are basically stand alones).

• 2000 Winter - New / Transformation - The Road to Become the Super Soldier (Shin / Henshin - Super Senshi e no Michi - Last Dracul Jokyoku)
• 2000 Summer Decisive Battle / The Forest of Transylvania - A New Arrival! The Soldiers who Protect Chibimoon (Kessen / Transylvania no Mori - Shin Toujou! Chibimoon wo Mamoru Senshitachi)
• 2001 Winter - Decisive Battle / The Forest of Transylvania [Revised Edition] - The Enigma of the Ultimate Enemy, Dark Cain - (Kessen / Transylvania no Mori [Kaiteiban] - Saikyou no Kataki Dark Cain no Nazo -)
• 2001 Spring - Last Dracul Final Chapter - The Seal of the Super Planet Death Vulcan (Last Dracul Saishuu Shou - Chou Wakusei Death vulcan no Fuuin)

If I try to give a “brief” synopsis on the Dracul series, I might end up writing a mini essay. Sooo..lets just go with the Dracul series features a smorgasbord of monsters and mythology from vampires to undead serial killers to werewolves to heavy Judaic references to the mysterious 10th planet, Vulcan. This series is probably some of the darkest material in Sailor Moon and sometimes most complicated storyline. (Just note that the the 2001 Winter revised edition of TnM acts as both a revision and sequel to help tie the story into the 4th show, so don’t skip it!)

Annnnd that got really long but I hope you end up watching these wonderful shows! They are probably my favorites of all the older shows. :)

@ree-fireparrot, I’ll be curious to see what you think after giving them a view!