Dear Busupasu,
As far as my knowledge goes, PF is applicable to your establishment under Section1(3) of the Act, once your establishment crosses an employee strength of 19 for the first time. The employee strength will include all employees working at all levels like teachers, support staff, peons, cleaning staff and security guards even if they are hired through a contractor.
For ESI Applicability, your establishment is not a manufacturing concern and hence the limit of 10 employees is not applicable. Being a non-manufacturing concern, the applicability depends on the state in which your establishment is located. State-wise the category of establishments and the employee limit is specified for non-manufacturing enterprises.
Note that if your school has a canteen within the premises employing more than 10 employees, ESI will be applicable to that canteen considering that it is a manufacturing activity.
Hope that it helps