If we talk about confidence, just money and privilege won’t provide it. Money and privilege produces arrogant, self-obsessed dunces, the likes of which are running this country at the moment. OP wants confidence for her kids, not arrogance.
Confidence encouraged by good education comes from both academic and social activities. My daughter goes to a private secondary girls’ school, my other two to a private coed primary school. Both schools, although quite academic, are not hot houses. The focus is on making children enjoy learning, discover and nourish their interests and strengths, and on giving everyone the opportunity to be good at something - music, drama, art, design, sport or the more academic subjects. The kids are not taught just to pass exams and are not tested non stop. They are not told they are the best - they are encouraged to do their best. If they are tested, the marks are descriptive rather than in the form of points or percentages that rank them relative to their classmates. Even parents don’t know how their kids rank relative to others. Tests are mainly for the teachers to plan the curriculum, to find out what the individual kids’ strengths and weaknesses are and to teach them accordingly. Smaller class sizes definitely help, as it means the teachers can pay more individual attention to students. Confidence comes from knowing that when you are good at something it is noticed and appreciated.
Socially, there is lots of teamwork, and the kids are taught to respect other kids’ opinions and differences - and of course the other way round: they know their opinions will be respected too. There’s a lot of debating, discussing, critical thinking. Also, feeling included does wonders to your confidence. My eldest daughter is mildly autistic, but she has never been labelled as such or singled out in class - instead, all the kids had a few lessons about autism, and about other conditions that mean people may act a bit differently from what we’re used to, but it’s OK. And nobody has ever commented in a critical way about my daughter’s occasional ‘weirdness’. She is confident if socially ocassionally awkward and shy.
Basically, confidence comes from self-respect. Find your children’s strengths, encourage them to do their best at what they are passionate about. Teach them to respect others and to have the courage to have and express their own views. Teach them to say no to things they are not comfortable with and to not give in to peer pressure.
I know it’s all a bit high-winded, but it works.