A few things for starters.
There is no universal law or set of laws regarding arms binding the 13 colonies in 1775 when the revolution begins. Each colony has its own laws.
The vast vast vast bulk of these laws are not gun control laws restricting the ownership of arms (although certain colonies did have laws against the enslaved being armed or learning gunsmithing) but rather militia laws that REQUIRED free, able bodies men of military age to own guns of a certain level of quality and with certain features that made them suitable for military service. So not only does the government require you to be armed, they require you to be armed with guns and gear that can go toe to toe with standard military firearms.
For my example I'm going to use Virginia, as it is the colony and later state that I have studied the most intimately, but most of the colonies had VERY similar laws.
In the first half of the 18th century Virginia's militia laws required all free, able bodies, non Catholic men between the ages of 16 and 60 to possess a functioning firearm, certain quantity of powder, and an edged weapon like a bayonet, sword, or tomahawk, plus powder and shot. This allowed for the use of civilian oriented arms like fowling pieces (shotguns) that most colonial farmers would have owned as farm guns anyway. The men were also required to attend militia musters for training when called upon by the officers of their county militia. If they could not afford arms those arms were supposed to be provided by local government.
In 1755 Virginia updated the gear requirements, stating that every man must have "a firelock well fixed, a bayonet fitted to the same" and a "double cartouche box," which is a simple wooden block with two rows of 9 holes drilled into it for carrying cartridges. They were also required to have, in addition to a certain amount of powder and shot, at least 6 rounds made up into premade cartridges. Compared to the pre-55 law, these new requirements are very very clearly trying to ensure that the militia are armed and accoutered in a manner close to that of professional soldiers. The primary difference between the fowling pieces I mentioned earlier and military firearms of the period were the fact that the latter could accept a bayonet, and were loaded with premade cartridges rather than loose powder and ball, as cartridges allow for much more rapid reloading. They also changed the training requirements to a monthly militia muster in each county to train the men.
So why the sudden emphasis on the entire military age population being equipped similar to professional soldiers? Things on Virginia's western frontier were getting spicy with the French, and the legislature understood that they needed to up their defensive game for the coming French & Indian war. This law was intended to get VA militia as close to a military standard as possible.
The 55 law was in effect from 1755 - 1771 when, due to significant tumult in the VA legislature caused by it's dissolving by Royal Governor Lord Dunmore, the law was allowed to lapse.
After Dunmore was ejected and Virginia had declared its statehood in 1775, they quickly set about re-upping the militia law with one really key difference: Rifled arms were now an acceptable substitute to bayonet bearing arms. The period between 1755 and 1775 had seen an explosion in the production of rifled guns on the western frontiers of Virginia, Maryland, and Pennsylvania (one inventory of arms taken in 1783 records that over 90% of private arms in Augusta county VA were rifled) and many European militaries had adopted rifle armed troops into their force structure as skirmisher/sharpshooter units. So much like the 55 law was intended to bring the VA populace up to a modern military standard, the 75 law sought to utilize the rifle culture of the frontier to bring VA militia force structure up to the new standard of militaries in 1775.
So all that establishes what the baseline was for gun related legislation in 18th c. America, so let's move on to the wording of the 2nd amendment.
"A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed."
Many of the founders clearly felt that militia was a necessary defense apparatus for the new nation, and based on the writing of their militia laws, they expected these weekend warriors to be armed in a manner similar to that of "real" soldiers. That said, not everyone agreed on the usefulness of militia, with George Washington being quoted as saying "to rely upon the militia is to rest upon a broken walking stick." Washington had been hung out to dry by these non-professionals one too many times, and that is reflected in the attitude he displays in the above quote. Still, looking at the generally accepted logic of the founders as a whole, they clearly felt that militia was necessary, expected that militia to have access to military quality arms, and since by definition, militia provide their own arms, the populace must have access to military quality arms.
I'm not going to make any attempt at a modern public policy argument for or against modern gun laws or ownership. Y'all are big boys and girls who can figure out the modern issues for yourselves, I'm just trying to help people get into the minds of the guys who wrote the 2nd amendment a little bit.