I don't think it's as much of a stretch from a Brown Bess Musket to an M-16 as it is from a printing press to radio and television. The former is a logical advance of technology, while the latter would be sheer magic to an 18th Century intellectual.
Be that as it may, the "assault weapon" of the late 18th Century was the Brown Bess or Charleville Musket. It wasn't particularly useful for hunting, although it would serve in a pinch. It had two virtues: It could be loaded and fired rapidly, and it could mount a bayonet. As has been noted, that's exactly the type of "arms" our forefathers intended us to "keep and bear."