Fit trumps selectiveness.
The right school for your child is the one which suits your needs and his needs best. How do you figure that out? By actually visiting the school. Try to do that while classes are in session. If at all possible, arrange an overnight if your child is considering a boarding school.
Now I can hear you thinking to yourself that the videos and the Skype chats were so wonderful that the school has to be perfect for your child. There's no need to visit. So expensive and so much trouble. Perhaps. But, you know how videos are produced. No matter how relaxed and casual they may appear, they show you exactly what the school wants you to see. A Skype chat certainly is useful and can answer many questions. However, and I cannot stress this enough, it is no substitute for actually experiencing the school during a visit. After all, you wouldn't buy a house or rent an apartment sight unseen, would you? Apply the same common sense to selecting a private school.
There are hundreds of gems out there.
For every Exeter, Andover or Hotchkiss et al, there are literally hundreds of fine private schools out there. Not all in the northeastern states either. How do you find these 'gems'? You search for schools on this site which match your requirements. Start by eliminating all the things you don't want in a school. For example, if you only want to send your child to a boarding school, don't bother looking at all the day schools in your area. Or if you feel that your religion is a really important selection criterion, then eliminate the schools which don't meet your needs. It will take some time but eventually you will identify 10-15 schools which you think might be a good fit. Whittle that list down to 3-5 schools which you are serious about. Visit these schools. Each and every one.
If you can afford a consultant, then this is one reason you need one. Your consultant will match your needs and requirements with schools which will be a pretty good fit. One of them will be the 'right fit'. That's what consultants do.
Determine what you need and want in a school.
While it is important to ask advice and listen to the opinions of friends and family, in the final analysis the school which you will select is the one which fits your needs and requirements. Think carefully about why you plan to make such a substantial investment in your child's education. What are you really trying to accomplish? Preparing her for college? Yes, a college education is important. But as you know very well after this dreadful recession we are still muddling through, a college education does not automatically guarantee employment. Wouldn't you be better running with your child's strengths? If she is an avid rider, then find a school which will allow her to excel at riding. Hockey? Situate him in the school which offers the best mix of ice experience and competition combined with solid academics. A private school can help its students identify a niche which works for them.
The beauty of the right private school is that it will bring out all kinds of attributes and possibilities which your child intrinsically possesses, but that you never thought would blossom. The right nurturing atmosphere can make that happen. A competitive school isn't the only place where you can achieve these kind of results. Those results and a happy child are what you are looking for after all. Don't ever lose sight of that objective.
Look beyond the competitive schools. They are not the only game in town.