<p>To answer the OP: go to a great public school and it won’t matter at all. Not one bit. I’ve served for many years on selection committees for graduate schools in my field and I assure you, it won’t matter.</p>
<p>If you are interested in an academic graduate program (Masters to PhD), go to an undergrad school where you can work with professors, do research, get great grades and letters of rec. And yes you can do that at small LACs or large research institutions. Just take some initiative while you are there. And any school worth going to if you want to pursue a PhD will pay YOU to go-- with tuition waiver and often a stipend. YOu can go to the Ivy Leagues for such a PhD and most definitely have first attnded a public school if you have a good GPA, did some research have good letters of recommendation and test scores. </p>
<p>If you are interested in a professional program, you’ll have to pay your own way but again, tons of great schools to choose from to make you very competitive for such programs. They need not be Ivy league.</p>