Once you understand the finances and have a firm budget, you will be able to make a list of schools.
You can get to medical school from any school on your list- that’s on you. “Keeping the financial part aside” is not realistic.
Keep in mind that many/most premeds shadow at home during breaks, and many begin with their pediatrician.
You will be seeking out volunteer opportunities- that is also on you. Keep in mind that many do not attend medical school straight from undergrad. They take time to strengthen their application, which includes working in underserved communities/populations.
Glad to hear that your state schools are on the list! Rutgers has a lot to offer.