As to what to ban, I think it’s instructive to look at what bans have been effective and what have not. First, with guns- full-auto capable weapons (that is, guns that can shoot multiple bullets with one pull of the trigger) were banned in the 80s (IIRC), and I think that this ban can be thought of as successful, because the vast majority of these mass shootings don’t involve full-auto capable weapons.
Why was this ban successful (largely)? I think the answer is pretty easy- because there weren’t that many full-auto weapons in private hands to begin with.
I think we can infer that banning things that are not common can be successful.
But banning things that are common, or easy to produce, has had an awful track record in America- prohibition of alcohol and then drugs are the easiest examples. Basically, there’s not much point to banning something that’s both readily available and has a high demand. A ban on semi-automatic weapons (weapons that shoot one bullet with one pull of the trigger), a category which includes most handguns and a very large percentage of long guns (rifles and shotguns), would probably be largely unsuccessful, because these weapons are extremely common.
A ban on high capacity magazines might fall in the middle ground- I don’t know how many of these magazines are out there. If there are millions and millions, or if they’re very easy to manufacture (for example, if someone can take two 10 round magazines and combine them in their garage with basic tools into a 20 round magazine- and I don’t know if this is true), then such a ban would probably be ineffective. If not, then perhaps it would be effective. It’s certainly worth looking into.
Without a way to get rid of the hundreds of millions of guns already in America, I think it’s pretty clear that a blanket ban, or a more limited ban on specific types of weapons (if they’re already common), would do little if any to reduce mass shootings (and probably gun crime in general).
I don’t know what the answer is. Perhaps an armed cop or two should be on duty in every school when class is in session. Perhaps we should even have a new uniformed service, specifically trained and dedicated to protecting schools. Some have suggested arming the teachers- I’m pretty skeptical, but some community in a state like Texas is bound to try this sooner or later.
Hopefully someone smart has some good ideas.