Well, I'll post here what I posted there about what the courts said in the Heller decision:

Well, according to the US Court of Appeals for the District of Colombia, Heller decision (case no 04-7041a). It is about hunting as well as self-defense:
page 46
“To summarize, we conclude that the Second Amendment
protects an individual right to keep and bear arms. That right
existed prior to the formation of the new government under the
Constitution and was premised on the private use of arms for
activities such as hunting and self-defense, the latter being
understood as resistance to either private lawlessness or the
depredations of a tyrannical government (or a threat from
abroad). In addition, the right to keep and bear arms had the
important and salutary civic purpose of helping to preserve the
citizen militia. The civic purpose was also a political expedient
for the Federalists in the First Congress as it served, in part, to
placate their Antifederalist opponents. The individual right
facilitated militia service by ensuring that citizens would not be
barred from keeping the arms they would need when called forth
for militia duty. Despite the importance of the Second
Amendment’s civic purpose, however, the activities it protects
are not limited to militia service, nor is an individual’s
enjoyment of the right contingent upon his or her continued or
intermittent enrollment in the militia.”

An interesting bit of the decision (page 53) which came up in the orals before SCOTUS, as the Attorney General for the US acknowledged he would be hard pressed to argue that the M16 or other assualt rifles aren’t protected under 2nd Amendment:

“The modern handgun—and for that matter the rifle and
long-barreled shotgun—is undoubtedly quite improved over its
colonial-era predecessor, but it is, after all, a lineal descendant
of that founding-era weapon, and it passes Miller’s standards.
Pistols certainly bear “some reasonable relationship to the
preservation or efficiency of a well regulated militia.” They are
also in “common use” today, and probably far more so than in
1789. Nevertheless, it has been suggested by some that only
colonial-era firearms (e.g., single-shot pistols) are covered by
the Second Amendment. But just as the First Amendment free
speech clause covers modern communication devices unknown
to the founding generation, e.g., radio and television, and the
Fourth Amendment protects telephonic conversation from a
“search,” the Second Amendment protects the possession of the
modern-day equivalents of the colonial pistol. See, e.g., Kyllo
v. United States, 533 U.S. 27, 31-41 (2001) (applying Fourth
Amendment standards to thermal imaging search).”

From the oral arguments before SCOTUS in Heller, and keep in mind that Atty General Clement was arguing in support of the ban:

JUSTICE SCALIA: But that opinion also, it didn’t use the militia prologue to say it’s only the kind of weapons that would be useful in militia, and that are commonly — commonly held today. Is there any Federal exclusion of weapons that applies to weapons that are commonly held today? I don’t know what you’re worried about. Machine guns, what else? Armored bullets, what else?
GENERAL CLEMENT: Well, Justice Scalia, I think our principal concern based on the parts of the court of appeals opinion that seemed to adopt a very categorical rule were with respect to machine guns, because I do think that it is difficult — I don’t want to foreclose the possibility of the Government, Federal Government making the argument some day — but I think it is more than a little difficult to say that the one arm that’s not protected by the Second Amendment is that which is the standard issue armament for the National Guard, and that’s what the machine gun is.
CHIEF JUSTICE ROBERTS: But this law didn’t involve a restriction on machine guns. It involved an absolute ban. It involved an absolute carry prohibition. Why would you think that the opinion striking down an absolute ban would also apply to a narrow one — narrower one directed solely to machine guns?
GENERAL CLEMENT: I think, Mr. Chief Justice, why one might worry about that is one might read the language of page 53a of the opinion as reproduced in the petition appendix that says once it is an arm, then it is not open to the District to ban it.
Now, it seems to me that the District is not strictly a complete ban because it exempts pre-1976 handguns. The Federal ban on machine guns is not, strictly speaking, a ban, because it exempts pre –
pre-law machine guns, and there is something like 160,000 of those.
JUSTICE SCALIA: But that passage doesn’t mean once it’s an arm in the dictionary definition of arms. Once it’s an arm in the specialized sense that the opinion referred to it, which is — which is the type of a weapon that was used in militia, and it is –it is nowadays commonly held.
GENERAL CLEMENT: Well –
JUSTICE SCALIA: If you read it that way, I don’t see why you have a problem.
GENERAL CLEMENT: Well, I — I hope that you read it that way. But I would also say that I think that whatever the definition that the lower court opinion employed, I do think it’s going to be difficult over time to sustain the notion — I mean, the Court of Appeals also talked about lineal descendants. And it does seem to me that, you know, just as this Court would apply the Fourth Amendment to something like heat imagery, I don’t see why this Court wouldn’t allow the Second Amendment to have the same kind of scope, and then I do think that reasonably machine guns come within the term “arms.”
Now, if this Court wants to say that they don’t — I mean — I mean — we’d obviously welcome that in our — in our obligation to defend the constitutionality of acts of Congress.
The one other thing I would say is that this is an opinion that is susceptible of different readings. It’s interesting that Respondents’ amici have different characterizations of it. The Goldwater Institute calls it strict scrutiny; the State of Texas calls it reasonable — reasonableness review.

I'll add here that the SCOTUS decision referred to allowing 'reasonable restrictions' and gave examples of groups- felons/mentally. They didn't mention banning types of firearms as examples of reasonable restrictions- but that is where the court fight will be in the future.