If you pick the right state as your home base and get a carry permit and then add one or two non residency carry permits you can get up to around 40 or so states to be legal with your handgun. Add a few more states that you can carry in your vehicle as long as it is not in easy reach of the driver and a few more that if you are unloaded and have the gun and ammo secured and you can get most of the states worth seeing. Stay out of NYC, NJ, California, Mexico and Canada. The rest check. I use a smartphone app called "CCW" that updates nearly every time I bring it up that tells you where you can carry and what the travel rules are.
The shotgun should be good most places accept NYC, Mexico, Canada.