The word mandatory is a little harsh.
In my dream world, the gov (state) would have an organized militia of the populace that trains for 6 weeks at the beginning, 1 weekend a month and 2 weeks every summer. This would be all volunteer, but government funded (arms, training, ammunition, first aid kits, etc). Every single member of the militia should have a new government issued select fire M16, and at least 1000 rounds in their home.
Since we're dreaming here, we could also say the militia is required to stay stateside (meaning they can NEVER, for ANY REASON, be called to go to a war in another country. their ENTIRE purpose would be to defend the USA from their home state.)
Firearm safety and training should be mandatory in all schools. (This at least would mitigate NDs and give some exposure to the general populace).
And no, the National Guard does not fill this dream as evident by the current number of them forced overseas.