Using university rankings is a bad way to pick a university to attend.
One issue is that the way that US News ranks universities is not likely to correspond to what makes a university a good fit for you. Some people want a large school. Some want a small school (such as what in the US we would call a liberal arts college). Some would rather be in a big city. Some would prefer a smaller city or small town. Some students want an academically demanding and potentially stressful school. Even some exceptionally strong students would do better with a less stressful school (and finding the right balance between academic rigor and stress can be tough in some cases).
Different schools are strong for different majors and are good fits for different students.
And there are a HUGE number of universities that are excellent for a premed student. There are almost as many that are very good for a CS major.
If you look at the students in a very strong MD program and look at where they came from, you will find that they came from a wide range of undergraduate universities. Where you get your bachelor’s degree is not all that important for medical school admissions. However, getting a strong GPA in tough premed classes is important.
Rutgers is a very good university. Rutgers is very good for premed students. Rutgers is very good for CS. It is perfectly normal for graduates from MIT or Stanford to find themselves working alongside graduates from Rutgers and U.Mass and San Jose State, and in at least one case that I know of some of the above were working for a boss who was a Rutgers graduate.
This gives me sort of a mixed reaction. First if you are applying to Rutgers in-state and if it is a safety for you, then it is a strong enough safety that it is okay for your other applications to be to reaches. However, once the acceptances come in, I hope that you attend a university that you can afford and that is a good fit for you whether that be Rutgers or somewhere else.
Doing very well at a university that is ranked in the top 150 or 200 will help you get into a very good medical school, provided that you also do well on the MCAT and get good medical experience and get great references.
@WayOutWestMom is an expert on medical school admissions. I agree 100% with her that which university you get your bachelor’s degree from is relatively low on the list of criteria for medical school admissions. In my immediate family we do not have any MDs. We do have three people who either got or are about to get or are studying for a graduate degree (master’s degree or doctorate) in a medical-related field. All of them report that the other students in their program came from a huge range of different undergraduate universities.
And I have worked in high tech for my entire career, and have worked with coworkers and bosses from a huge range of universities. In most cases no one cares where you got your degree.
You would be best off to attend a university that is a good fit for you and that allows you to get your bachelor’s degree with no debt. Whether this is Rutgers or somewhere else might not be easy to determine and finding a good fit is likely to need some careful thought.
And I would be very, very cautious about taking on debt for a bachelor’s degree, particularly for someone who is considering medical school and for whom a school as strong as Rutgers is available as an affordable option.