I wouldn't concern yourself with "tiers." As you suggest, it is hard to know how these tiers are determined. There are many knowledgeable people on this forum. I would suggest that you post some information about your child and what type of school you are looking for, geographic considerations, etc. and you will probably get some good suggestions. You can also work with an educational consultant. Here is the website for their professional organization -
Independent Educational Consultants Association - just be sure you get someone who specializes in prep school admissions rather than college admissions.