5. What the fandom writes
Fix-it for the train station — the largest and most emotionally charged category. Rewrites the S3 finale so they don't separate, or so Finn follows her to New York, or so Rachel comes back. These fics are essentially love letters to the idea that they should have stayed together.
Future fic / New York — Finn in New York, building a life alongside Rachel's career. What does he become? How does he find purpose in a city built around ambition when his own ambition is quieter and more local? These fics do interesting work on Finn's identity outside the quarterback-teacher-director identities the show gave him.
Post-"The Quarterback" grief fic — Rachel processing Finn's death. Largely pre-saga but atmospherically important. These fics established "He was my person" as the fandom's central phrase, and established the specific texture of Rachel's grief: loud in public (the tribute performance), silent in private (unable to look at his things for months).
High school AU — Rewriting their meeting in different contexts: they weren't in Glee Club, or they met at a different school, or one of them transferred. The core is always the same: the quarterback who should be with the cheerleader, choosing the theater girl nobody else sees.
Domestic/established relationship — The fandom's comfort food. Finn making breakfast. Rachel running lines while Finn pretends to listen but is actually watching her. The specific domestic pleasure of two people who fit together at the places where they don't match.