It really doesn't make much difference which college you go to as far as what specialty of medicine you ultimately want to practice.

The better question would be, which college is the best one to go to if you want to become a doctor. Overall, medical school is still fairly competitive, and the better the reputation of the college you attend, the better off you'll be, assuming your grades and MCAT scores are the same. Having said that, though, the colleges that have a reputation of a high acceptance rate into medical school may "weed out" their undergraduates - meaning that the pre-med classes are especially difficult. In that case, some people who may get accepted to medical school are actually discouraged from applying. Also, some top caliber schools grade their students very harshly, meaning your GPA may be lower at a top school than it would have been at a college that is just above average, but not top-top.

So, what I suggest is that you talk with counselor, select a range of colleges to look at from ones that are possibly out of your reach, down to a safety school or two. Try to get information on the schools to get a sense of how difficult the pre-med track may be and how successful they are in placing students into med school. Go to the school that you like the most, and are accepted to (obviously you have to include financial issues into the assessment).

As for wanting to be a pediatrician - you'd go to college as a pre-med (typically 4 years), taking the required classes for med school. You'd need to apply to med school near the end of college, and once accepted, you'd go to med school for 4 years. Near the end of med school, you'd apply for a residency program in pediatrics. Pediatrics is not very competitive of a specialty right now. Once done with medical school, you'd do a residency in pediatrics which is 3 years. You are paid during residency, but not much, especially considering the hours you'll work.

Once done with residency, you'll be able to practice pediatrics.