Schools come under about four kinds of ownership:
State owned (called "state" schools in the UK, "public" schools in the US), meaning they're supported by the state and tax-payers
Private not-for-profit, meaning any proceeds - whether fees or donations- go back into the school for facilities, materials and salaries
Private individually owned or owned by a corporation, meaning all funds go to the individual, company or subsidiary they've set up to handle those funds. The school is then funded by that entity, which entirely controls whether there is ample or inadequate money available to run the school.
If you are looking at a privately owned school you should make sure that there is a good working relationship between the owner or education group and the head/principal. After-all, the owner/education group is more likely to be profit orientated, particularly if they have invested heavily.
You should also establish if the school has a proper PTA, ie: one that is active and influential, not just a group of well-meaning parents organising coffee mornings and cocktail parties. In addition, is there a proper board of governors (or equivalent) and established accreditation? Just being an IB World School isn't full accreditation by an independent organisation.
If the school you have chosen, or possibly has been chosen for you by the organisation you are working for (or an agency working for them) doesn't have the above, you need to ask yourself: how and to whom do parents address serious concerns?
For example, what's your recourse if you child is threatened with expulsion if you continue to air your dissatisfaction of a teacher? Or, what if you are not being informed about serious incidents that might effect your child's safety? Perhaps another child's behaviour is seriously disrupting your child's education. If you aren't happy with the answers perhaps you should look at a different school.