Three of our children attend an excellent private school which my brother and I also attended (many!) years ago. Our eldest has flourished there, really come into his own taking advantage of so many of the opportunities on offer - but interestingly very much in his own time. Initially he was wary of over-commitment and worked hard on the academic stuff, biding his time to leap into the unknown. This came relatively late, after several years of us wondering whether his laid back approach was really what we had hoped for when sending him there!
But you have to trust your children, give them the tools and opportunities and be there in a supportive - NOT a driving - role.