I agree with the "quality" comment.
I happen to be a big fan of private colleges/universities, as the experience was much more in line with what I wanted (mentorship similar to graduate school, attention to detail, small faculty:student ratio, all classes were taught by professors, etc). With that being said, there were some limitations, mostly access to large-scale research. While I think I was a more competitive med school app (obviously I chose a diff. path in the end), large universities offer a host of opportunities not commonly found at smaller institutions.
I'd recommend checking out a range of colleges/universities, and going where you "fit in" the best. Oh, and try to avoid debt if at all possible. The cost of an undergraduate education can be ridiculous. My alma mater would have been prohibitively expensive ($40k+/yr) if I wasn't on academic scholarship, though some large public universities have priced themselves into private college/university ranges.
Btw....the "prestige" really doesn't matter as much for medical school, though it can open doors, depending where you are looking.