I'm one of those people who chose my undergrad institution based on price and not ranking. After attending public school in K-12, I came to my undergrad because financially it was the best fit for me, but I don't feel that has given me any disadvantage in applying to grad school. I've worked very hard here and I am pleased with the graduate institutions to which I've been admitted. Don't assume that someone with high aspirations was born with a silver spoon in his or her mouth.
That being said, I know that there are some quality institutions out there not in the top 50, and I wish you great success.