Man arrested for 2x4 labeled "High Powered Rifle"
Obviously there are limits, just like with any other Constitutional right, but there is no other Constitutional right that people are trying to "interpret" straight out of existence. You don't hear people saying "privacy is of greater benefit to criminals than law-abiding citizens, and we'd all be safer without it, and our government is stable and benevolent, so the concept of a right-to-privacy is an outdated principle that we should just ignore because the Founding Fathers were living in a different time."
And yes, it absolutely applies to modern firearms, just like the right to free speech applies to modern communication systems like email and Twitter.
The rule created by DC v. Heller is sensible. Any weapon that are "in common use for lawful purposes" of self-defense, hunting, and sport. This includes the AR-15 but does not include hundred-round drum magazines for the AR-15. What I would like to see:
(1) Universal background checks for all transactions, new or used.
(2) Some form of mandatory training.
(3) Permanent bans on firearms ownership for anyone with a history of felonies or domestic violence (already in place).
(4) Greater access to mental health records as part of the background check process (recently put in place by Obama).
(5) Bans on magazines over 10 rounds. I'm not sure it'd matter that much, but the impact on lawful uses is so minimal that I support it as a "let's see if this helps" attempt.
(6) No bans on AR-15s or other semi-automatic civilian firearms adapted from military firearms (regardless of their origin, they're time-proven and effective designs for both hunting and sport, such as the Remington R-15 small-game hunting rifle and the Remington R-25 large-game hunting rifle). Heck, most of good pump-action shotguns on the market were derived from military and police designs; doesn't mean they're not well-suited for everything from shooting ducks to breaking clays to home defense (Remington 870 and Ithaca 37, I'm looking at you).
(7) Darned-near-close-to-a-ban on fully-automatic or burst-fire weapons (this is already in place).
(8) More law enforcement resources directed to addressing gang and drug violence (the primary source of homicides in the US).
(9) More law enforcement resources directed to patroling public areas such as malls and schools.