Does the Naval Academy better my chances of joining the most elite force of America, the Navy SEALs?
The Academy will put you in a great position to become a SEAL Officer. If you would like to go straight to BUDS, then enlisting would be your best option. The difference would be that you would not be going in as an officer.
Does one have to be selected to go Marine option at the Naval Academy, or is it the cadet's choice?
You are ultimately selected based upon a preference list you submit your junior year. If you are interested in going Marines, there are certain training events you can take part in during the summer to set yourself up for that option.