Personally, I interpret it to mean that all citizens have the right to bear personally-owned "arms" in order so that they may participate in a well-regulated militia... not that the guns themselves have to be owned by the militia, but so that the citizenry may participate in that militia. Coincidentally, this sorts well with the idea that there were few, if any, permanent Federal arsenals in the 1780s.
As to the definition of "militia" in this case... keep in mind that the rag-tag collection of Minutemen on the village green in Lexington, MA, was a "militia" in the classic sense of the word... a loose, under-trained paramilitary organization manned by citizen-soldiers.
Now, in a more modern sense, "militia" is rightfully attributed to the National Guard and various State Guards or State Militias we see at-present, however, applying the word "militia" in the classical sense is also correct and in-keeping with American tradition.
Heck... the Selective Service registration system can be construed as a "militia" of sorts insofar as it enrolls young people of fighting age and regulates its composition by providing legal penalties for failing to register to be part of that dormant pool of warrior stuff.
And, of course, by only a small stretch and well within the bounds of legality, good taste and reason, it can even be argued that the entire population of the United States is a Militia-of-the-Whole or a Militia-at-Large or a Militia-of-Last-Resort for such purposes.
After all... if we are invaded and the defense does not go well...is there the slightest bit of doubt in any rational mind that we would call-up that Militia-of-Last-Resort... our very own Volkssturm of underage/overage/female cannon-fodder to fend-off the barbarians?
In addition to the Guard and organized State Militias and active paramilitary groups, this so-called Militia-of-All-Citizens is "well-regulated" through FOID and CC laws and licensing.
Close Enough for Gubmint Work...
