I think it should be 21 years and up to own a gun.
Why?
Though a 16 year old can think of the consequences, and certainly know every wrong aspect, they are not always 100% likely to take it seriously. Especially since they will most likely not be sent to jail for shooting one person, since they are under the age of 18.
Then again, why not just have it at the age of 18? People are mature at that age, right? Not always. In my opinion, for a person to reach their full maturity level, and learn enough about life, they need to be 21. At 18, not everyone has the responsibility level they need yet.
But then again, there are some people who are considerably responsible for their age, and could have owned a gun at age 13 and done quite well with it.