If American politicians were at all reasonable, they would stop talking about banning guns vs. making it easier to acquire them. One simple and reasonable solution to the gun problem is to start treating guns like cars. If you want to own a car, you have to register it. You are also required to take a written test, to demonstrate that you know the laws regarding its operation. Then you have to take a driving test, to demostrate that you can safely operate the vehicle. Finally, you are required by law to carry liability insurance, so that if you happen to injure another person while operating your vehicle, the insurance will cover the cost of their medical bills.
When an individual decides that they want to own a gun, they should first be required to produce a license, showing that they have passed a written test, demonstrating that they know the laws about gun use, and that they have demonstrated the ability to safely operate a firearm on the range. The purchaser should also have to provide proof of insurance. Then, the gun ought to be immediately registered in the purchasers name upon sale.
Simply requiring gun-owners to carry liability insurance would make it much more difficult for certain people to acquire firearms. If a person has a history of domestic violence, for instance, insurance companies will be reluctant to sell them liability insurance. The more of a risk the individual is, the higher the cost of insurance will be.
Furthermore, the government could impose a differential sales tax on firearms. There could be a 6% sales tax imposed on the first three firearms one purchases, with the purchase of a fourth firearm raising the rate to 8%, and the purchase of a tenth raising it to 50%. This would effectively discourage the accumulation of firearms. Furthermore, you could encourage people to purchase biometric guns (guns programmed to only fire with the fingerprint of the registered user) by letting the sale of these weapons have a 50% discount on the sales tax rate. You could also give tax credits for the purchasing of gun safes and locks, to encourage best safety practices.
It should also be required for law-enforcement officers to personally carry insurance on firearms issued to them by the police department.