It's not really a case of punishing anyone. Some people may be perfectly capable of driving through a town at 150MPH. But, a lot of people aren't so the law prohibits it for all. The vast majority of gun owners may be perfectly responsible, But there doesn't seem to be any way of telling who is or isn't before an event. We seem to be stuck in a sort of all or nothing attitude. What's needed is some form of middle ground between guns for all and a blanket ban.

My suggestions would be:
Compulsory training and testing before being issued with a license.
Continued training on a regular basis, (I don't know what frequency that should be).
Re-testing every five years
Severe penalties for anyone selling a gun to someone who doesn't have a license with the onus being on the seller to ensure that the gun is registered in the new owners name before handing it over.
Accountability for every round of ammunition purchased.
Gun theft to be treated as a serious crime, (not only in terms of sentencing, but also the effort put into recovering them).
Practice shooting to be restricted to registered firing ranges, (this would aid accoutability of amunition).
Age restriction, (probably 21 but I don't know).

None of the above could be achieved over night, so there would need to be period between announcing these rules and enforcing them in order to give people the oportunity to comply.
There also needs to be some sort of attitude change. In most other countries, if you have a child who's not fitting in well at school, has become something of a recluse with no friends, and seems to be bullied, we tend to encourage extracaricular activities where they can meet new people and make friends. We don't try to cheer them up by buying them a semmi-automatic rifle and encouraging them to take it to their next show and tell.

For one requiring you to keep track of any guns you purchase unless they are legally transferred to an eligible buyer. I would like to see a heavy fine for allowing your gun to be stolen and if it happens too often you should be determined to not be a responsible gun owner. Of course there will have to be some allowable exceptions. Laws that place further restrictions might be considered but only if research indicates they will cause more good than the inconvenience. The first thing that needs done is serious research. I want fewer gun deaths. I also don't like laws based on emotion, even though that is how most laws get passed.