I don’t know anything about military high schools. So I’ll come at this as a fellow parent with a DD who received offers of appointment to three SAs, and a DS who’s awaiting his own SA decisions.
If you’re looking for a military school that might give him an edge in terms of SA admissions, there may not be such a sure thing. There may be some military schools that send a disproportionate number of grads to SAs, but that might be less causal and more coincidental (i.e. students with strong military interest self-select into those schools). In any case, I’m not sure choosing a high school because it’s believed to confer some SA admissions advantage is a very good idea.
If for whatever reason you’re looking to go outside your local public school, I’d suggest finding whatever school will allow your son to thrive the most in terms of academics, athletics and leadership. May be a parochial school, a private prep, a magnet school, a charter school, a military school. And even home school, which is what many cadets/mids have done.
Ultimately the SAs want to know, regardless of the kind of school, that the candidate took the most challenging courses available and excelled at them. And they want to know that the candidate is prepared for the academic rigors unique to SAs. So again, whatever school brings out the very best for your son — that’s where he should go.
DD went to middle school at a small Catholic all-girls school with high-end academics, athletics and arts. If not for a job-related move, she would’ve done high school there too. After our move, she ended up at a small non-denominational coed private school. In many ways it was quite similar to her prior school, but also very different. But this much I know: Regardless of which high school she attended, she would’ve ended up exactly where she is now — USNA. And that’s because, without a bit of military connection, each school brought out the very best in her.