I think it depends on what time period this is set in, or what time period it resembles. If there's a kind of 'military academy' at all, it probably isn't middle ages, right? Maybe take a look at what happened for 18th or 19th century military. I think most of the officers there were from the noble class, and the typical 'officers and gentlemen'. Of course, that's only for European history, I don't know how it would work in other cultures. But the idea I have is to maybe see if you can find a description or even curriculum for a British Empire-era academy, and go from there.
Otherwise, it might depend on which branch of the military they're going to, like army vs. navy etc.
A lot of good suggestions here already. Maybe something like learning military protocol and signaling, too?