Well, for me, a great backstory is key. If a companion has a rich past filled with events that shaped them, like Eder's time in the war, it makes their story interesting. It gives a context to their actions and attitudes in the present of the game.
Character development also matters a great deal. A companion whose story shows growth and change over time, like Aloth dealing with his identity crisis and evolving as a result, makes for a great story. Their journey from where they start to where they end up in the game is really important.
Xoti's story is quite remarkable as well. Her faith and her role as a priestess are central to her character. Her journey with the Watcher is filled with moments of self - reflection and growth. The way she deals with the darker aspects of the world while maintaining her positive outlook is a great part of her story.
Aloth is another character with a fascinating companion story. His struggle with his own identity, being a wizard with a dual personality, is a central part of his narrative. His journey to come to terms with himself and his place in the world makes for a great story as you play through the game with him.
In my opinion, the Ranger class can be great for the story in Deadfire. Rangers have a strong connection with nature which often ties in well with the game's themes and story elements. Their animal companions also add an interesting dynamic to the story progression.
Pallegina has a very unique story too. Her connection to the Vailian Republics and her sense of duty are central to her story. Her conflicts between her personal beliefs and the orders she has to follow add a lot of intrigue. Also, her cultural background gives a different flavor to her story compared to other companions.
Their personality also matters. A character like Wyll, who is very chivalrous and has a strong sense of justice, can influence the moral compass of the story. His decisions and the way he interacts with the other companions based on his personality can lead the story in different and interesting directions.
One of the best FNV (Fallout: New Vegas) companion stories is Boone's. His backstory of being a sniper in the NCR and his tragic past with his wife makes for a very engaging narrative. It adds depth to his character and his actions in the game.
For me, Lae'zel's story has a lot of emotional depth. She is a githyanki warrior, and her story is full of her struggle to uphold the values of her people while also seeing the flaws in their ways. She has to deal with her own sense of identity and where she belongs in the grand scheme of things, which can be really moving at times.
The diverse personalities of the companions are a big highlight. You have the sarcastic and clever Sebille, the noble - yet - flawed Red Prince, etc. Their interactions with each other and with the player - character are full of humor, drama, and tension. Also, the moral choices presented through their stories, like whether to help Fane in his rather ambiguous quest, add depth to the gameplay.
Piper is a great choice for the story. She's a journalist with a curious nature. She'll often comment on the events in the story, adding some interesting perspectives. And her personal quest also ties in well with the overall narrative of Fallout 4.
Gale is another good one. His story is filled with magic and mystery. His relationship with the Weave and his past mistakes make him a very interesting character to have around during the story. He often provides insights into the magical elements of the game world, which can enhance the overall story experience.