Batman himself is obviously a must - include. His leadership and skills are central to the Batfamily dynamic. Also, Robin, especially Damian Wayne as his complex relationship with Batman adds a lot of drama. Nightwing is popular too, with his acrobatic skills and his own journey away from being Robin. Batgirl, like Barbara Gordon, is often included for her intelligence and fighting abilities. And Alfred, the ever - loyal butler, who often provides support and wisdom to the family.
Definitely Batman and Robin are the most common. But also Red Hood, Jason Todd, has a huge following in fanfiction. His redemption arc and his sometimes - tense relationship with the rest of the family make for great storylines. Oracle, Barbara Gordon in her post - Batgirl role, is also very popular as she can offer a different perspective and her computer skills are invaluable. And then there's Cassandra Cain, her unique fighting style and her struggle to fit into the family make her an interesting character to include.