LEAD: The absolute best book for Nicole Zajack was the one in which Dawn moved into her new house and she and the other baby sitters became convinced there was a ghost rattling around. It turned out to be a playful mouse. ''That was great,'' said Nicole, who's 13. ''Dawn's really neat. She's just like me.

The absolute best book for Nicole Zajack was the one in which Dawn moved into her new house and she and the other baby sitters became convinced there was a ghost rattling around. It turned out to be a playful mouse. ''That was great,'' said Nicole, who's 13. ''Dawn's really neat. She's just like me. She's on the quiet side, but she's definitely mature. A very neat person.'' After she read the fifth book, Nicole began to phone her local bookstore every day to see if the next one had come in yet. ''I mean, I couldn't wait,'' she said. ''Who could?''

''I sit glued to the books,'' said Kathy Ames, who's 12. ''They're not out-of-the-ordinary stories, like a space creature lands in the yard. I like books that are realistic.''

Nicole and Kathy, along with just about every 8- to 13-year-old American girl alive, are rabid fans of the ''Baby-Sitters Club'' books. Among the fundamental principles for their age seem to be that they must giggle at the mention of boys, learn to play the piano and have read ''Logan Likes Mary Anne!,'' ''Karen's Roller Skates,'' ''Claudia and the Phantom Phone Calls'' and the 18 other books in the series. Otherwise, they're just out of it.

The books, which are currently the most successful paperback juvenile series in the country, trace the adventures of a group of spunky eighth-grade girls who run a baby-sitting cooperative in the fictional town of Stoneybrook, Conn. Kristy is the club's president. Three times a week, the girls get together after school at Claudia's house. They go there because she is the only one with her own phone, which they can use to get their bookings.

Each novel details the escapades of one of the members, often a taxing baby-sitting assignment. There was the time, for instance, that Jessi baby-sat for a deaf boy and hastily had to learn some sign language. In another book, Kristy's mother remarried and the new family moved into a neighborhood where the kids mocked the Baby-Sitters Club and, worst of all, teased Louie, Kristy's aged pet collie. On yet another occasion, Jessi baby-sat for...