Third, it is a long commitment. And your choice of residency is also not guaranteed. Some get their first choice; others don't. That may also depend on, guess what? Needs of the Navy.
Fourth, be careful about telling USNA and/or your BGO that you want to go to med school right after USNA. The mission of USNA is to produce line officers and they don't want to admit a bunch of mids who want to be doctors. Thus, it is viewed unfavorably. I'm NOT suggesting you lie. I am suggesting that you be FULLY prepared to go into an unrestricted line community.
I agree with many of the above points, but I'll reiterate or clarify a few things. Yes, don't tell your BGO about the med school thing. For some reason they have a huge hangup about it. Bottom line, the Navy loves Academy doctors because they are more likely to stay in 25+ years (I'll post the link if I can find it).
I disagree about the officer vs doctor mentally. Navy doctors ARE officers. They lead divisions and departments and commands just like line officers do. I expect all military officers to be role models, not just line officers. In fact, a Navy doctor is more likely to be on the ground in Iraq than a SWO or NUKE.
Also, USNA has consistently had 15 spots for med school. Generally they come from chemistry majors, but as long as you take the med school pre-reqs (organic chem, biology - this may require summer school), you'll be fine as an economics or english major (due to the BS instead of BA degree).
The applications and admissions to med school happens concurrently with service selection. The 15 candidates USNA picks for med corps usually are very qualified for med school (high GPA, MCAT, ECA's, LOR's), so the chances are pretty small that they won't get in. In the case where someone who gets a med school spot from USNA, and doesn't get accepted to med school, one of the other candidates will get a shot.
Getting into med school from USNA is difficult! You'll be competing against (I'm guessing here), 50 mids at the start. Probably half will give up after general chem (first year). For some reason mids hate chemistry. The remaining 25 or so that will do well through organic and the rest of their courses are on the right track to be competitive. Now remember there are only 15 spots, so, like usna1985 said, be prepared to enter into different warfare community if things don't go your way. Or maybe better advice would be to be proactive and fix your shortcomings before you are out of contention.