I went to a relatively good school - a grammar technical - many people have made a decent living by being educated at a Grammar school.
Our daughter went to a Newcastle private school - she won a scholarship. A cynic would say that private schools have scholarships to attract the best brains and keep up their exam grades. A realist would say they have scholarships to achieve charitable status and pay less tax.
A good education certainly helps; but if you want to get on - who you know is just as, if not more, important than what.
If you really want to get on; go for a public school - the more exclusive the better.
Really really want to get on - join one of the public school semi-secret groups (gangs) or that extreme of exclusivity the Bullingdon club.
Want your offspring be a Prime Minister and control people? Get him into Eton. Eton has spawned nineteen PMs and counting.
If you cant get to good school, buy your qualifications on the web; or try that school in London that teaches the desperate how to get rich,
Never forget though - all good schools have limited membership.