Applying to BS is a preview to college application process… many families/ students hunt for the top tier schools. You can do this of course but keep in mind you might get shut out completely.
It is not where you go but what do can you once you get there. Many many boarding schools have excellent course offering and teachers. Many have very cool extra curricular pursuits. Do not overlook the schools just below the top tier.
And, when applying/interviewing, show your curiosity and your humility. Most applicants are great students and motivated. Schools want to know more about you and how you might dive in, thrive, explore, contribute, and enjoy life within their whole community.