You can major in anything you want to. But there is a set list of classes that most medical schools will require that you complete as an undergrad, before you apply. I don’t have the current list off the top of my head, but as I recall it was 2 years of bio, a year of inorganic chem and organic chem, a year of higher level math, a year of physics - and now, I think it includes a semester of bio chem. There may be one or two other classes. Most schools offer all these courses - and you’ll still need to self-study for the MCAT so it’s all fresh in your mind for the test. There are no ‘programs’ at schools that you need to take and prestige is really not of great significance.
To get a sense of how competitive admission is, check out the AAMC stats for admission to medical schools:
https://www.aamc.org/data/facts/applicantmatriculant/157998/mcat-gpa-grid-by-selected-race-ethnicity.html
Hope this helps.