As we know from DH, the Grey Lady and the Bloody Baron were both alive at the time of the Hogwarts founders. My question is simple, are they the first of the Hogwarts ghosts or did older ghost gravitate towards the school once it was established as a sort of safe haven?

Better yet, why do the ghosts haunt Hogwarts? Other than Moaning Myrtle and Professor Binns, none of them died on the grounds (that I’m aware of) so why stay at Hogwarts?

Also, the house ghosts? Were they elected? If not, how are they chosen?