"which clearly places the right with "the people"It clearly does. Not with "the citizens". Not with "all persons".
"I think it's hard to read "people" as anything but an individual right."
Let's accept that. Then how do you read "arms" for these individuals? I see no limitation.
I think I would limit it to arms that a person could bear but would have to look at the 18th Century meaning of "arms" to be certain. It would also not cover any arms prohibited to the US by treaties, since Article VI makes treaties the "supreme law of the land" along with the Constitution and laws passed at the federal level.