As a warm foreign friend to the USA, and a concerned grandparent of US citizens, I wish I could think that you will find some way of reducing the incidence of massacres of your innocents, but I am not optimistic. The second amendment, the incredible number of guns in circulation already, the value placed on violence in your* culture, the value placed on celebrity, however brief, in your* culture, the grossly inadequate cultural and institutional response to mental illness, the degree of dysfunction in your political system at the moment - all these and other misfortunes make it seem that the maximum degree of "gun control" of which you are politically and culturally capable, while desirable in itself, may not have much impact. To be specific, a large-scale mandatory gun buyback, as done in Australia, would seem to be out of the question, but, in some lines of argument, essential if you wanted to make a real difference. I fear the next horror will be even more appalling.
Everyone responds from fixed positions - the constitutional fundamentalists won't be able to consider the possibility that the second amendment is simply a problem that needs fixing, the people who value their guns and rightly don't consider themselves dangerous to anyone will desperately nitpick the statistics that show, clearly enough, that more guns mean more deaths, the people who hate guns will think that government can fix it by legislation (in the regrettable absence of a virus that selectively eliminated all those southern rednecks). And so on. It is one of those areas where a meeting of minds is difficult to achieve. Intelligent and decent people will say, for example, that "guns aren't the problem, people are the problem", or suggest that the appropriate response would be to arm teachers and give them weapons training. I would regard both of these positions as ludicrous. To respond only to the first - given the kind of problem that more than enough people are, and are likely to remain, having massive numbers of guns around doesn't seem like a good idea.
How to achieve a starting point for discussion? Maybe with an admission that we (by which I mean I, of course - your mileage may vary) don't have the answer. I was impressed by the 12 facts statistics linked above. They reminded me of RSL's definition of street photography - that it doesn't lend itself to an obvious or simple narrative. They don't give unalloyed comfort to either side in the debate.
*I know it isn't just you - our culture too, in different ways, whoever we are.