Most states will have you undergo training in order to carry a concealed weapon (ie carry in public).
What I'd actually favor is creating a two-tiered national licensing system. Tier 1 is buy any semi-automatic firearm you want and concealed carry in all 50 states. Once you get your license, no more background checks when buying firearms, no waiting period, no silly shit like magazine capacity. In order to get your license, you need to qualify on a pistol and rifle, assemble and disassemble the firearms, and demonstrate competency in regards to safety (no flagging, can safely load and reload, fix and clear a jam). All your background checks happen when you get your license, and if you are convicted of a crime, you lose your license or have it suspended as appropriate. Go ahead and cross state lines with your weapon, carry in all 50 states, and all person-to-person sales simply require that you show your license to one another. Tier 2 gets you any item you want, including automatic weapons. Basically, the same stuff applies.