Ok.... I am a Brit but my sister was born here. She did what you are talking about doing. Just so you know there is no such thing as "duel" citizenship. Unless you renounce your citizenship here, the US will always see you as American. Once you get your UK passport, then the Brits will see you as British and not care about the US side. When you leave the US it will be on the US passport as well as when you return. Once you are over in the EU then bounce around on the UK passport.
It will not affect your ability to purchase, sell or own firearms in the US.
