Would it be beneficial to major in Nursing with a minor in Psychology to become a neonatal nurse practitioner or any type of nurse in general? Are there any other major/minor combinations that are recommended?

It is not necessary to minor to become a nurse practitioner. I think it is wiser to put all your efforts into your nursing major to get a higher GPA. This will then better position you when you apply to graduate school. You should also be looking for nursing programs that offer the Doctor of Nursing Practice degree. This is the terminal degree for Nurse Practitioners. Some schools offer an "early entry" option where you take advanced courses within your undergraduate curriculum allowing you to progress easily to the graduate level.