You can't purchase it from a FFL dealer, unless it's for a rifle, like a pistol caliber carbine.
It's totally legal for you to own and carry. Michigan law allows it. Your options are to lie and say it's for a Hi Point carbine or something, or to have someone else buy it for you, the latter being the way I believe is legal. (You could also actually buy a carbine, but that would probably be a bit much)
Then, when you turn 21, and they ask "handgun or long gun?" you can give them some crap and say "machine gun".
A good way to save money, save the hassle at your age, and to have lots of ammo, is to take up reloading.