The first two problems would be easily prevented by keeping your firearms in a safe. If you're worried about arguments with your spouse becoming fatal, please talk to a counselor ASAP.
As for negligent discharges, which are probably the most legitimate concern, you should always follow the four rules of gun safety:
1. Treat all guns as if they are always loaded.
2. Never let the muzzle point at anything that you are not willing to destroy.
3. Keep your finger off the trigger until your sights are on target and you have made the decision to shoot.
4. Be sure of your target and what is behind it.
In my experience, these are hammered into civilian students who take firearm training classes, but soldiers in the military often haven't heard of the four rules and generally are far more casual with their guns than civilians.
As for negligent discharges, which are probably the most legitimate concern, you should always follow the four rules of gun safety:
1. Treat all guns as if they are always loaded.
2. Never let the muzzle point at anything that you are not willing to destroy.
3. Keep your finger off the trigger until your sights are on target and you have made the decision to shoot.
4. Be sure of your target and what is behind it.
In my experience, these are hammered into civilian students who take firearm training classes, but soldiers in the military often haven't heard of the four rules and generally are far more casual with their guns than civilians.