Well, it can be a good idea to read the Doom Patrol comics first. They often provide more depth and detail to the characters and storylines. But if you're more into visual experiences, the TV show or other adaptations might also be a decent starting point.
One great Doom Patrol fanfiction is 'The Unlikely Heroes'. It really delves into the characters' backstories in a new way. The author gives a fresh perspective on how the characters interact with each other outside of the main storyline. Another one is 'A New Beginning for Doom Patrol'. It's interesting because it takes the team on a completely different adventure, full of unexpected twists and turns. And there's also 'Doom Patrol: Redemption Arc' which focuses on the characters' growth and how they overcome their personal demons.
The 'Doom Patrol: Crawling from the Wreckage' is also great. It delves deep into the characters' backstories and their struggles with their powers and identities. We get to see how each member of the Doom Patrol copes with being an outcast in society due to their abnormal abilities. It's a story that really makes you feel for these complex characters.