You have to have a license to drive a car, why not a gun? The federal government should establish training prerequisites, background check standards, a basic mental health screening process, and a national database for licensees. The states can then use this information to establish their own programs with nationwide reciprocity requiring all citizens that wish to carry a gun (concealed or not) to carry a license.
Licenses could be multi-tiered based on qualifications (Rifle, Handgun, Concealed) and revoked for criminal or mental health problems. Such a system would ensure that we have a responsibly armed population without infringing upon second amendment rights.