We should decide which species can join. Humans may comprise the majority, with others in specialized roles or in locations where their skills assist, such as elves stationed near a forest military base. But a military group for another species might work very differently, with humans a minority or not allowed. Use the world view of both the species and this military to decide if it’s a good fit among them. As mentioned in Creating Places (italics), joint settlements and sovereign powers can exist, implying a species melting pot and leadership is shared, which can lead to joint military groups, too. If elves revere life but a group doesn’t take prisoners, preferring to kill them, we can assume elves don’t join. The prerequisites may be designed to eliminate them, either for world view or physical reasons. A knighthood might require using a lance, eliminating a dwarf.
This raises an important point: not all members of the military are fighters. Those in a modern Navy on Earth are unlikely to engage in hand-to-hand combat, but in the Age of Sail, they were expected to if boarding or boarded (or on land excursions). In the case of our life-revering elves, perhaps they are the equivalent of doctors. Such details add believability to a military, where good uses can be found for species with specific traits and concerns. Isn’t it good to show that the elves are there but in a typical role, and perhaps the dwarves are, too, operating artillery like catapults? They can be officers, too, as they seldom fight. There are plenty of support personnel who also don’t.
Consider whether members of any religion are part of the military, in what capacity and what rank they have. They might be fighters, healers, counselors, or all three. Today we’re all aware that soldiers become traumatized and need psychological support, but even if our world is too barbaric for that sophisticated level of support, soldiers die, and many will desire last rites.
Whether they’re still active, alive, or long dead (and revered or despised), notable members are figures that our characters can aspire to be like, or dread being compared to. All we need is a name, a reputation, and the deed that caused their fame, plus maybe a sense of how long ago and well-known this is. We benefit from at least one good and one bad member, one to cause pride, another to cause shame for members. It’s realistic. People can simply fail to do a job, or they can do something deliberate, such as betray their fellows and run from battle. If we have a specific set of job functions this group performs, have someone fail in that, as this makes the character more memorable.