While congress did have the power to raise a standing army, it did not until it appeared that state militias were not equal to the basic task of fighting a war. Congress raised and equipped armies during the revolution, and even then, many of the troops were state troops. A basic problem not otherwise relevant to any of these issues was that some states were richer than other states, to put it plainly, and the poorer states had more of a struggle to equip their own troops. Of course, at the time, a so-called standing army did not have that ancient a history. Typically, armies were raised only when needed, which was more of a feudal practice, and there was a well-defined system in place to raise those armies when needed, although those armies were not large by today's standards.
During the later colonial period and on into the revolutionary war and afterwards, there were state troops that were essentially full-time soldiers in some states but I've seen very little recent references to any such troops. I mention this only because there is the assumption that the only state troops that existed were local (all militias are local in our sense) militias. But that does not seem to necessarily be the case.
In Virginia, for instance, which may be the only such case, there were troops stationed along the frontier. This I picked up from readings in very old books that I was not reading for anything about militia history but for other reasons. Those troops, which I believe may have been called rangers, apparently did not exist in large numbers, nor did they operate in anything like a company sized unit. But up and down the Allegheny Front and beyond, there were large numbers of settlements built around forts. The troops seems to have just been there to supplement the settlers when there were troubles with Indians and those troubles seem to have been constant in those areas up until the 1790s.
Some of those attending the constitutional convention, all politicians in a way, were involved in the militia in one way or another, the best known being Washington.
Shoot low, sheriff. They're riding Shetlands!
Underneath the starry flag, civilize 'em with a Krag,
and return us to our own beloved homes!
Buy War Bonds.