But does that mean all the people all the time and all "arms"?

That is the core of the debate isn't it. On the one hand, some believe that the Amendment's phrase "the right of the people to keep and bear Arms" creates an individual constitutional right for citizens of the United States. Under this "individual right theory," the United States Constitution restricts legislative bodies from prohibiting firearm possession, or at the very least, the Amendment renders prohibitory and restrictive regulation presumptively unconstitutional. On the other hand, some scholars point to the prefatory language "a well regulated Militia" to argue that the Framers intended only to restrict Congress from legislating away a state's right to self-defense. Scholars have come to call this theory "the collective rights theory." A collective rights theory of the Second Amendment asserts that citizens do not have an individual right to possess guns and that local, state, and federal legislative bodies therefore possess the authority to regulate firearms without implicating a constitutional right.

I personally lean towards the individual right theory. I think you should have the right and capability of protecting yourself anywhere anytime. Schools are gun free zones yet people get shot there for example. It's obviously a complicated issue. Education seems to be the answer to a lot of our problems.