From "Concerning the Militia":
"To oblige the great body of the yeomanry, and of the other classes of the citizens, to be under arms for the purpose of going through military exercises and evolutions, as often as might be necessary to acquire the degree of perfection which would entitle them to the character of a well-regulated militia, would be a real grievance to the people, and a serious public inconvenience and loss"
This pretty clearly carries the implication that being "well-regulated" is more than just well-equipped.
It is, however, clear that the intention was to continue the policy of citizens bearing arms, even treating that as an implicit part of the culture of the time. Madison says, in "The Influence of the State and Federal Governments Compared", as an offhand remark, "Besides the advantage of being armed, which the Americans possess over the people of almost every other nation, ...", and in comparison to Europe, it is expected that Americans can be trusted with guns: "Notwithstanding the military establishments in the several kingdoms of Europe, which are carried as far as the public resources will bear, the governments are afraid to trust the people with arms."