On money: It is a wonderful thing to see what can be done for a school when immense amounts of money are wielded by people with good hearts, good minds, and - most importantly - good sense. (Any public school principal would drool.)
My children are lucky enough to attend a school (Mercersburg) where a couple of very rich and very grateful alumni have had an extraordinary impact (also thanks to great planning by the head of school). Facilities are spectacular, financial aid is generous, and faculty are well paid. But before the money was there, the culture, spirit, whatever is the appropriate word, was already alive, or the school would not have had the powerful effect on its alumni that has made those who can afford it give so generously.
On tiers: 1) What Albion said. 2) More of what Albion said. “Second-tier” schools can be full of “first-tier” teachers/administrators, and they have plenty of “first-tier” students as well. 3) Size matters. A student at a school of 400 is likely to have more opportunities to shine, and to shine earlier, and to try new things, than a student at a large school whose population is skewed toward high achievers. 4) Some schools are not considered “top” schools by the kids/parents using that term simply because of their location outside New England, so unless you live in New England and want a short drive to your child’s school, look to the schools outside that region. 5) Bottom line: It will be your child’s home, so (as best you can) make sure it’s a good one and that it feels like a possible home to your child. Don’t worry about the numbers; wonder about the people.