You may be looking at the 13 Colonies as much more similar than they actually were. They were, and thought themselves to be, 13 different, governmental entities, which later each became a "country" or "state", that then bound themselves together. This is important to remember because the answer to your question depends upon which colony that you choose. Virginia was a commonwealth and had a royal governor, New Jersey was a royal colony and Ben Franklin's bastard son was the last royal governor there, while Maryland was a proprietary colony, so had a governor appointed by Lord Calvert, and so the governor wasn't a "royal governor". PA was proprietary colony, run by the Penn family, and was heavily Quaker. Four colonies, four different ways of doing government.
So to be precise, (iirc) 12 of the 13 colonies had militias. "Minutemen" were formed from Colonial Militias, but did not exist in every colony. So every Minuteman was in the militia, but not every militiaman was a minuteman.
As an example, the colony of Pennsylvania, for most of its existence, did not have standing militia regulations, due to Quaker influence, so no standing militia there.
The Minutemen that most folks refer to, are a New England idea, and the ones that fought at Lexington and Concord were from Massachusetts. Not all of the colonials who fought against the British at those battles were "minutemen", for by the time that the British reached Concord, enough time had elapsed for more than the minute companies to form in the town. (Minutemen were only 1/4 of the actual militia)
So regarding your firearms question..., depending on the colony, the eligible male might have to provide his own weapon, or as in Maryland, sometimes he would be issued a musket and a bayonet and cartridge box, sometimes not. The muskets owned by colonial governments were older models of the King's Musket, and were kept in colonial armories. They were not owned by the crown. (In fact the Royal Governor, Lord Dunmore, was chased out of VA when he got caught with British Marines trying to steal the colony's property..., the powder supply in the powder magazine in Williamsburg.)
Sometimes the eligible male had to provide his own gun, and that was most often a fowler (no bayonet capability), smooth bore. It was much rarer for a man in 1775 to "own" an actual King's Musket, than most folks realize. To get one you either had to have purchased one from the colony IF the colony actually owned some and would sell it, or the musket at one time was awarded to a soldier who mustered out of the regular british army to become a colonist, and was given the musket as a partial benefit of taking that offer. Not a very common thing.
Rifles, for the most part, were a PA, Western MD, and VA gun at the start of the war. That's where the riflemakers were, and rifles were quite expensive at the time.
So a "safe" answer is that without picking an actual colony, most men that owned a gun, owned a fowler. IF instead they were armed with an actual musket, it would've been a variation of what is called today, "The First Model Brown Bess". Several companies make very serviceable copies of either type of firelock.
LD