But maybe the OP is referring to minimal ship complement to carry out Galaxy-class missions for Starfleet. That would be different.
I was talking about the minimum requirement for a fully-crewed Galaxy
-class starship ready to carry out missions. Basically, all the Starfleet personnel with none of the civilians attachments or passengers.
I think the 800 figure is more reasonable than the figures below 500. While the Enterprise
was indeed much more advanced than Kirk's ship, the size of the ship begs a larger crew. According to Sternbach's TNG Manual, there are two sickbays in the saucer section, for instance. Or, the engineering personnel required to maintain the ship.
Yes, on person could operate the ship a la "Remember Me," but I was speaking more about a fully-crewed ship.