Military groups and their members are often known for their weapons, skill using them, or both. A distinctive choice makes them more memorable and entertaining. Think of the light sabers Jedi wield in Star Wars, or the phasers from Star Trek. There are special weapons in fantasy, too, though seldom by an entire military, presumably due to manufacturing limitations, but we don’t have to abide by that. And weapons don’t have to be spectacular to be associated with the military.
Do they all have a two-handed sword because they specialize in fighting something like giants? If they’re archers, we can decide whether bows are always made the same way, using wood from one type of tree or another. It sounds better when we’ve invented the tree and can write something like, “Kier lowered his solanaen bow as the loosed arrow slammed into his nemesis.” With repetition, naming the type of material helps associate it with a mythic quality. Audiences begin to wonder why we mention it and how such an item is special, even if it’s really nothing.
At a minimum, we should decide what weapons are required and bestowed by the military (and replaced by it if broken or lost in the line of duty). On Earth, members were sometimes required to supply their own weapons and armor; not having them would prevent inclusion.
We can also determine their preferred weapons, such as a long bow instead of crossbow despite having proficiency in both. Do they prefer a short sword to a long sword? What weapons do they rarely use? Are there any for which they have contempt? Snobbery exists in all things and a master swordsman might find a bashing weapon crude. A sense of their outlook and missions help us determine these. If we can’t decide now, return to it later when we understand this military group better.