What do selective/well known boarding schools look for in a candidate?

Agree with everything @Golfgr8 said.
I would also say, overall, they are looking for nice kids who are good students and like to participate. They want kids who can work well with others in groups, who have passion for anything and show commitment; They are looking for good students ( not the best students as we first thought) but good students who will work on their academic interests; Finally they want kids who want to belong to a community. They don’t want kids who do a single thing, or kids who aren’t interested in other people. And, finally, though they won’t say it, I think they want to avoid kids who might create havoc for whatever reason.