General Discussion

The text of the 2nd guarantees "the people," rather than "the states," the right to keep and bear arms. What seems to be forgotten in analyzing what this meant at the time of the original Founding is that the first eight amendments to the Bill of Rights, as originally conceived, only restricted Federal actions. It would therefore be true to say that at the time of the founding, the states retained total authority to regulate guns (The original limitations on state power are found in Article I, section 10). However, they did not possess this authority because the 2nd Amendment protected their right to regulate, but rather because the 2nd Amendment's "right of the people" would have only protected the people's right from encroachment by the Federal government. You could say the same thing about the other Amendments. For example, the First Amendment only prevented the Federal government from forming a national church; individual states could and did have official government religions. That Amendment also only restricted the Federal government from restricting individual citizens' right to assemble or speak, while states could restrict those rights as they pleased (Limited only by their own state constitutions).

Since the states didn't give away their power to regulate their own citizens' guns, they retained the power to regulate them as they wished. Functionally, the 2nd Amendment prevented the Federal government from regulating private citizens' firearms ownership; states could muster armed citizens into militias, arm selected citizens for militia service, or choose other forms of local gun control. The 2nd broadly protects individual firearms ownership; such broad protection effectively maximized states' ability to form militias. Even a dirt-poor state which couldn't afford to run a centralized, organized militia would nevertheless have the ability to leave private firearms ownership legal, with no federal interference. Such a state could then muster the privately-armed citizens.

However, once the 14th Amendment is passed, the whole applecart is upset. Once the Supreme Court used it to "incorporate" the Bill of Rights, restrictions that once only prevented Federal action now acted to prevent both Federal and state actions. Therefore, a right "of the people" now established a right that no government entity in the United States could take from any citizen. The Founders didn't think that this was how the Bill of Rights would function, so looking back to their interpretations of how it functioned is at best disingenuous. Considering that 14th-Amendment incorporation is generally understood as a broad extension of the Bill of Rights against state governments, it's very odd to look at people writing about the Bill of Rights before incorporation existed.

Edit: As for the Second existing so as to give citizens the ability to fight the government, it would probably be more accurate to say that it was partly designed to ensure that the states could retain some military capacity to counterbalance any federal military. OP seems to say that.