Apart from hunting, why does an American need a gun unless it's to do damage? You want to shoot a gun, go to a shooting range, you want to shoot something more powerful, join the military. Target practice? get a paintball gun or something, and shoot some cans, I don't know...
Ban them all except hunting rifles, and make the process of getting one very thorough. Improve gun education.
Illegal guns will find their way onto the streets, there will still be murders of course, but there needs to be a cultural shift. This mentality of "it's in the constitution" must change, and changing a country this big, and stubborn in their ways will take generations, but it has to start somewhere.
Just my opinion