How are the multiple bands of each branch organized and staffed?
Regarding the other military band programs, most particularly the Army, I'd suggest you do a Google on "Army Band Programs" and surf the web.
There is specific information on the web that is up-to-date. Anything I talk about here might be dated and no longer applies.
The upshot is, the services no longer target high-school level musicians. They are after college graduates, conservatory students, or well-seasoned and experienced professionals.
If you're thinking of the Army, you need to talk to a recruiter. Be aware, however, that most recruiters don't know their butt from a hole in the ground when it comes to the Army band program - so if you get one of those, I'd suggest you politely decline to talk to him until HE gets up to speed.
In the final analysis, you will need to take an audition. The audition generally consists of scales (all majors and all three forms of the minors), a prepared solo that shows contrasting styles, and probably some sight reading. If you double on another instrument or sing, be prepared to demonstrate those skills as well -- you get additional "points" for that.
If you pass your audition and you're afforded an opportunity to enlist for a current slot, that's fine - the rest is up to you and your recruiter (remember to get all promises in writing). If, however, there is no current slot, you'll be put on a waiting list and contacted when a slot opens up.
The Army runs its own School of Music now. For decades, it was tied to the Navy's School of Music. The Army's interest is to have musician Soldiers as highly skilled as possible, and then to receive military-oriented training at the SOM (how to march, manual of instruments, etc.) then go out to their band within 6-8 weeks.
Good luck.
U.S. Army, Retired (built mid-1950s)
Adams E2 Euph (built 2017)
Boosey & Co. Imperial Euph (built 1941)
Edwards B454 Bass Trombone (built 2012)
Boosey & Hawkes Imperial Eb tuba (built 1958)
Kanstul 33-T lBBb tuba (built 2010)