I think random, but that would be an awesome way to go "back to the beginning." Even the ghost of Catherine the Great there! (I assume she died when the school blew up, presumably destroying the trophy.)
Though I know they couldn't really pull it off then (though they might've made it work with some heavy cosmetics and weird explanation), have Jenny Calendar among the ghosts (extra irony since Giles momentarily thought Jenny was haunting the school).
Might make it more awkward if like the janitor guy (don't know why I think of him that way) claimed he was cleaning the school during Graduation when they blew it up...collateral damage in the war on the Mayor come to literally haunt Buffy, among others.