Should I major in Molecular Biology?

Okay, so I know I want to go into a science field after I graduate. I am very interested in a career in either genetics or forensic science, and so I think that a major in Molecular Biology (or a major in Biology with a concentration in Molecular/Cell Bio) would be a good way to start pursuing either of those careers when I enter college. Would a major in Molecular Bio make sense for my career goals?

Then, when I go to graduate school, what type(s) of graduate programs would be good for someone who wants to go into either genetic research or forensic investigation?

Yes, a major in molecular bio makes sense for those career goals.

For genetics research, go to a grad program in genetics or human genetics.
See this link for info on forensic training and careers: http://www.aafs.org/students/student-career/pathologybiology