Answer is, "It depends." As with any Constitutional issue, this one is an issue of original understand and intent of the framers.
For example, freedom of speech doesn't mean you can go into a schoolroom and start yelling whatever you want. That is not what the framers meant by "freedom of speech."
See what you just did? The question was, what books (objects) can the government ban, and you went on about yelling (an action) in a schoolroom. I submit that shooting a gun in a schoolroom is against the law. The object in question is legal, the action is what is illegal. The proper analogy then is, as with books, which ones can the government ban? Can the government limit the number of books, or number of pages withing each book that a person can own?
The problem with trying to use a free speech analogy to guns is that any law to regulate guns is an infringement. And the right to keep and bear arms is the only one which specifically proscribes any infringement.
For example, it might be worth researching whether there was some clear way to distinguish between the meaning in the 1700's of "arms" and things like cannons. Did the framers mean cannons when they spoke of the right to bear arms? Stuff like that. (Again, NOTHING, like what the socialists are doing because they generally don't seem to care what the Constitution says or means.)