If we regulate guns like cars, then:
Anyone who passes a simple safety test (simple enough that the bulk of the population has little problem with it) can purchase a firearm and use it (subject to safety regulations) in public.
With or without a license you can own and use a gun on private property.
There are certain quality regulations on cars/guns which apply to using them outside private property (i.e., if it's likely to burst into flames, you can't take it onto public roads).
There is no federal regulation, except for rules saying that a license in one state is valid in all other states (i.e., a Texas CCW license works in NY).
This sounds like exactly what the NRA regularly lobbies for. The only people who will argue against your proposal are gun control advocates (e.g., Bloomberg).