I would be cautious about putting too much weight on GPAs as there is so much variation from school to school (which is why SAs tend to recalculate). Even with a recalculated GPA, the SAs will need to look at class rank, academic environment, strength of schedule, etc. when evaluating a candidate's GPA.
From the USNA Admissions FAQ... Q: "What Grade Point Average do I need to get an appointment?" A: "There is no specific GPA minimum. However, you should strive to be at least in the top 20 percent of your high school class."
SAT/ACT , and Class Rank are more meaningful than GPA. As to classes taken, take the most challenging classes you can.
And to answer the age old question of whether its better to take an AP course, or take a lower class and get an A, the answer is always --take the AP course and get an A. There's no way around it -- Admissions is going to look first and foremost at whether you have the academic ability to attend and graduate.
Not sure why you wouldn't take the USNA.edu site as the key source of information. They aren't making it up.
You should take the most advanced STEM based courses your school offers. Those are the key courses USNA looks to see if they are on your record. The SA's realize not every school has honors/AP/IB programs and they will compare your high school's resume to the resume of other high schools to smooth out the comparison of GPAs.
The vast majority of appointees have taken high school math to include calculus, science to include chemistry, physics, and biology (and many have taken 2-4 years of these type courses).
Realistically, if your GPA is less than 3.7 you better be bringing something else significant to the dance. A 3.7 GPA will not impress anyone on the admissions board by itself. The TWE threads are full of candidates with 3.9 GPAs (unweighted) with multiple AP/Honors/IB courses and great SAT/ACT scores. They just might have the misfortune of living in super competitive areas and didn't stand out elsewhere.
Cerberi and Old Navy are are spot on. Our DS applied with a 36 ACT and 1580 combined SAT and did not get an appointment on his first try. (he was a successful re-applicant on his second try). He was home schooled so there was no 'real' gpa or class rank to speak of. So, toss out gpa and class rank and what is left? Test scores are important as noted, however, the whole candidate score in all the others areas needs a very, very long look and effort. We were not sure how competitive his region was however, you should be working on a plan B too.