How many people on board the Enterprise were Starfleet personnel?
I've always figured it varied drastically at any one time. The internal space of the Ent-D is truly vast, and there is no reason to believe she could not comfortably accommodate 25,000 people if necessary.
If the usual complement is more like 1000 or so (as suggested on-screen) then it could include big mission-specific detatchments, like extra security teams, scientists, politicians or diplomats, some of who would be Starfleet and some not.
Maybe 500-600 core Starfleet crew?