Well, what is your home state?
The national universities are research universities and would have those opportunities.
Not sure what you mean by “establishing good connections”. If your goal is med school, then networking won’t really matter.
Have you talked to your parents about how much they’ll spend each year on college?
Any good school is fine for a premed. The goal is a high GPA in both science/math courses, and the overall cum GPA.
What do you think you’ll major in? You can major in anything you want as a premed. What is your favorite subject?