I think it's intended to do both because (A) the distinction between the two was not as large as it is today and (B) the Constitution before the 14th Amendment did not bind states in the same way that it did after the 14th Amendment, thus allowing states to work out the distinctions we are trying to work out at a federal level.
One page I looked at, since you are demanding specifics, says that "bearing arms" was often a euphemism for going to war. That suggests a militia interpretation with local control. Remember that the Constitution also requires that Congress reauthorize the Army every 2 years because it opposed the idea of a central standing army. In fact, the Virginia Declaration of Rights in 1776 (a predecessor of the Bill of Rights) states, "That a well-regulated militia, composed of the body of the people, trained to arms, is the proper, natural, and safe defense of a free state; that standing armies, in time of peace, should be avoided as dangerous to liberty; and that in all cases the military should be under strict subordination to, and governed by, the civil power."
But the 2nd Amendment also protects a person's right to keep arms, which suggests allowing people to take arms home with them. From a pragmatic standpoint, I would argue that during the period when this was written, it would be assumed that a person would take a firearm home with them and hang it over the mantle but not keep a canon in their barn.
And I suppose I should point out, again, that the Constitution opposed the idea of a standing army. I don't think the Founders intended people to take canons (or tanks or bombers) home to fight the government but expected the government to not have a large standing army with canons (or tanks or bombers) that the people would have to fight if they needed to go after the government. It's not practical to allow private citizens to own weapons that can do the sort of damage required to overcome a modern army but as the Founders designed the Constitution, there shouldn't be a modern standing army for them to have to overcome.
If so, then it's awkward to define "arms" without going through some contortions and finding some hidden definition in the second amendment that just isn't there (eg., "arms" are weapons that are carried).
"the Constitution before the 14th Amendment did not bind states in the same way that it did after the 14th Amendment"
While it's true that some amendments in the Bill of Rights were "incorporated" under the 14th, the second amendment was not.
"But the 2nd Amendment also protects a person's right to keep arms, which suggests allowing people to take arms home with them."
It protects the right of "the people" to keep arms, yes.
"I don't think the Founders intended people to take canons (or tanks or bombers) home to fight the government but expected the government to not have a large standing army with canons (or tanks or bombers) that the people would have to fight if they needed to go after the government"
True. But the people were expected to "repel invasions", and an invading army would have them. The second amendment had to protect large weapons also.