You are using a classic separation of the clauses in the Second Amendment but after District of Columbia v. Heller it has been interpreted as a single statement, with the first clause supporting the second. If you read it using the common meaning of terms at the time it was written, "militia" means a group of citizen-soldiers raised by a call to arms -- before we get to the second clause, this could mean the arms are owned by the State and given to them or they are owned by the citizenry. The second clause states:
the right of the people to keep and bear arms, shall not be infringed.
This answers the question left, of who owns the arms -- the people who keep them. This should make sense. The United States would not exist as it is unless the Revolutionary War militia had not themselves owned guns and been able to respond to a call to arms. It is also one reason that any invader of the United States today would be stupid to try and why the Swiss all keep arms in their homes. Sure, military technology far outstrips what a simple gun owner could do but as Iraq and Afganistan have shown people armed can put up quite a fight.