I dont know what county you are in, but you will probably need a "pistol purchase permit" which allows you to purchase a pistol. If you wish to carry it concealed you need a concealed carry permit. Depending on the county it usually isnt muchh of an issue beyond the application and fingerprints. Durham county has its own set of rules. They do require a regestration though, since I dont live there I dont have much of a clue beyond that.
woodsman gave you a good reference. As to the loaded shotgun on the back seat, I see little problem as long as it is in plain view. Pretty commen around here in the country.