The AR platform is a good starting point for you till you know what you want.
The receiver is the gun, so different configurations and calibers and platforms do not require additional firearm registration.
If you want a factory gun, then you can't form 1 and build yourself, you will have to hook up with a NFA dealer to order you one.
For a newbie I would get a facytory Rock River Arms short rifle.
This will get you started, you can change configuration later. When you order the rifle get a silencer on order for it also, an 11.5" sbr with silencer will be the same size as most folks semi auto carbine.
Cousino Firearms in Toledo is who I reccomend, but you probably have a dealer closer.