I got the impression that Myrtle was actually the only death, because it was when that happened that they sort of decided to shut down the school because it was too dangerous.
Parents wouldn't want their children in a school where'd there'd been one murder, let alone 3 or 4...
Okay more specific details on the timeline in lexicon:
-------------------------------------------------
circa May 1943: Tom Riddle learns to open the Chamber of Secrets and releases the Basilisk.
Myrtle, a Hogwarts student, dies in a second floor bathroom after seeing the Basilisk.
June 13: Hagrid is falsely accused of opening the Chamber of Secrets.
Aragog the Acromantula is released into the Forbidden Forest .
circa July: Tom Riddle commits his first murders: his father and grandparents in their Little Hangleton mansion.
circa September: Tom Riddle meets with Professor Slughorn and asks him about Horcruxes.
Tom Marvolo Riddle creates his first Horcrux: the diary.
-----------------------------------------------------
So IF we want to be by the book we have to be in mid-September, perhaps between Riddle's conversation with Slughorn and the creation of the horcrux.