Rankings change from year to year. You don’t change what university you are attending to accommodate any changes in rankings as they occur. Once you are a university student, you are going to be way too busy keeping up with class work to care at all what the most recent magazine says about the ranking of whatever school you attend.
And your chances of ever getting to medical school or to any other very good graduate program really will not depend upon whether you attend Brown, or Yale, or Duke, or Stanford, or UNC, or UMD, or UVM, or U.Mass Amherst, or most likely U.Mass Lowell. Some strong students might find themselves in the middle of the pack at the top ranked schools, and in the top 1/2 of the pack at the medium ranked schools, and the top 1/4 at lower ranked schools, but getting to medical school is going to depend a lot upon the student and very little on which undergraduate school they attend. Of course there will be someone who will be at or near the top of the class even at the tougher and higher ranked schools, but they would most likely have excelled as long as they attended any school that was a good fit for them.
As I see it, there are three possibilities:
One possibility is that you would qualify for a LOT of need based financial aid at Brown, and at other private schools that meet full need. It sounds like this is not the case.
A second possibility is that your family is perfectly comfortable paying somewhere around about $900,000 for eight years of university with no hardship at all and no debt at all. If this is the case, then really do not worry about the cost of Brown. Brown is a great university.
The third possibility is that you would need to take on some debt, or at least cause your family some discomfort, on the way to paying something like $400,000 for a bachelor’s degree plus something like $500,000 for an MD (remember that any graduate school is well into the future, and costs are going up over time). If this is the case, then right now is the time to be thinking about more affordable options.
Personally I was a much stronger student in my major and closely related fields, and a much weaker student in some classes that were required to meet the “general requirements” for getting a bachelor’s degree at the school that I attended. For me somewhere like Brown that allows quite a bit of flexibility might have been a better choice (but I went somewhere else, oops – too late to fix it now).
Rankings really do not matter. The difference between premed required classes at a school that is ranked in the top 5, versus premed required classes at a school that is ranked 16, versus premed required classes at a school that is ranked in the 100 to 150 range, is a lot less than you are thinking. At that last set of schools, there will be plenty of very, very strong students in the premed classes. There will also be plenty of homework and plenty of very tough exams at any of these schools. The top 10%, and probably more like the top 25%, of the students at the school that is ranked in the 120’s are going to seem very similar to the students at Brown or Duke or Harvard or Stanford. A lot of them will be very good students. They will however be human and subject to imperfections, and any of them might sometimes miss a question somewhere.
Duke has better basketball. Brown will require a slightly better winter coat.
Both can be great schools for a premed student, but only IF the family can easily afford it and still be able to help a LOT with the cost of medical school. Both will have premed classes full of very, very strong students.
Welcome to any highly ranked school, or to premed classes at a rather wide range of schools.
Some students get into these tough classes and find it to be a drag. Some students get into these tough classes and find that they love it. For some students both will occur but in different classes. You sort of need to show up at university and just see how it goes.
Definitely if you are taking any premed required classes, you will want to show up on day 1 planning to put in a strong effort. Staying ahead from day 1 is a very good habit to get into. This also applies to students who are not premed students but who are in majors that overlap with premed classes. Mostly this also applies to university students in a wide range of majors at at wide range of universities.
I do not think that your chances of getting accepted to a very good medical school, or to a different very good graduate program, will vary significantly regardless of which of these two excellent schools you attend. The only exception would be if in some way one turned out to be a way better fit for you than the other.
Every medical school that I am familiar with, and every DVM program that I am familiar with (medical but with different patients), and every highly ranked graduate program that I am familiar with, takes students who graduated from a very wide range of undergraduate universities.
Finding an undergraduate university that is a good fit for you, and where you will be comfortable, and sticking with a budget, are important.