I'm not enlisted, but I'm enlisting soon and might do something similar. In order to be an MP at least with the USMC, you need to be 19 so put that into consideration. I dont think you get to choose the job you are assigned to as an MP too. You might be out on patrol like a regular cop, or you might be stuck at a gate all day letting people through. Is it a good job? If you want to be a cop after you're done like me I imagine it would be a good choice because it will make getting hired by the police department way easier because to them you'd have experience in the field.
Hope that helps,
Mike