I'm skeptical of AM programs, having been through one myself. I feel like the options you have immediately after school tend to be extremely limited. Most companies and airports prefer to hire people with finance and business degrees rather than aviation management degrees, mainly because a lot of the schools that offer aviation management don't offer any hands-on experience training.
Definitely get an internship and as much hands-on experience as you possibly can. People tend to want to see what you have done rather than what degree you have.