Let's try to make a guesstimation from first principles.
There are a thousand children to be educated, supervised, nourished, and cared for.
When I was at school, the basic operational group was about 25 pupils, which, in 1970s to 1980s Romania, was called a class. I don't know how this basic group of pupils is called in English, so I'll go with class. Such a class goes through a full 4 or 8 year cycle mostly together; so for example, I started at my general school in class 1st B and ended eight years later in class 8th B. Then at highschool I started in class 9th D and ended four years later in class 12th D.
So, there are 1000 ÷ 25 = 40 basic groups of pupils. Since we know that a complete cycle is 8 years, this means that we have 40 ÷ 8 = 5 parallel classes in each year, Hogwarts 1st A, Hogwarts 1st B, Hogwarts 1st C, Hogwarts 1st D, Hogwarts 1st E, Hogwarts 2nd A, ..., Hogwarts 2nd E, Hogwarts 3rd A, ..., ..., Hogwarts 8th E.
We need at least one teacher, professor or supervisor per class at all times during lecture and individual study hours; let's assume that the schedule is 6 lecture hours, 6 individual study hours.
Since there are 40 classes attending lectures in parallel, we have at least 40 teachers or professors. Most usually, they won't do 6 hours of teching per day every day of the week, so let's multiply that with 1.5: we have a purely teaching staff of 60 teachers of professors. Some of them will have assistants or technicians; let's say maybe 30 assistants or technicians.
For the individual study period we need 40 supervisors to look after the pupils. We need a little more than 40 to account for sick days, holidays, and so on.
The teaching staff need secretaries to keep track of schedules, grades, lists of pupils, diplomas, payroll and so on. Where I worked back when, there were two of them for a staff of about 50; but Hogwarts is British, so we'll put 8 secretaries.
Then we needs cooks to feed those 1200–1300 people, plumbers, handymen, janitors, cleaning staff. I guesstimate one cook and one cleaning person for 50 people, 1 plumber, handyman and janitor for 100 people.
The school has extensive gardens, sportball fields, forests and so on. Let's put 50 gardeners, gamekeepers, field maintenance personnel.
Add in a minimum security staff, at least to patrol the fence and control the gate, say three shifts of 5 people plus 5 people extra to cover for sick days, holidays, or emergencies.
Finally, let's add 12 footmen and general men-at-all-works.
Over and above the functional personnel the school probably has some support staff -- accountants, librarians, printers (or scribes, don't know), medical personnel, carpenters, etc. Let's say 30 support personnel.
|Teachers or professors
||Includes physical education instructors etc.
|Assistants or technicians
||Take care of laboratory equipment, prepare experiments and so on
|Supervisors or proctors
||Look after the pupils after hours
||Keep track of paperwork and schedules
||Feed the pupils, teaching staff, administrative staff
||Keep clean, wash clothes
|Plumbers, handymen, janitors
||Perform maintenance of the school and equiment
|Gardeners and other outdoorsy personnel
||Maintain the gardens, sports fields etc.
||Control the gate, patrol the fences
||Do whatever needs to be done
||Accountants, librarians, medical staff, etc.
||People on the payroll of the school
So that overall there are some 350 people, more or less, working for the school. Plus of course the headmaster, assistant headmaster, their secretaries and servants... And speaking of servants, it is likely in the fictional interwar English landscape depicted in the films that every professor or teacher has their own servant.