Adam Kraut, a Pennsylvania attorney specializing in firearms law, breaks down the legal morass surrounding traveling with the good stuff.
Starting at about the one minute mark in the above video from The Gun Collective, Kraut walks you through the basic rules on carrying a short barreled shotguns, select-fire/full-auto weapons, short barreled rifled and destructive devices and the forms needed to travel.
Note that AOWs and suppressors have (slightly) different rules.
Plus keep an eye out for state laws (i.e. Illinois Nazis).
Adam, who by the way is running for the NRA BOD next year, has done a bunch of these informal videos on the legal side of NFA items and firearms law in general.
Below are installments on trusts and stripped receivers if you have a few spare minutes and an interest in either.