Discussion on the Military Organization and Capabilities of Various City-States
Can we discuss the armies of the various city-states and our headcanons with them? I'll start.
Noxus We know they have a Noxian High Command with some noble lineage. From the Rek'Sai writings we learned Noxus is based off the Romans (gladitor pits, currency, 'Empire').
I Imagine them to have armies similar to what is found in Warhammer's Imperium of Man. They would probably have Legions or something similar, private elite armies led by a High General, and augmented by a massive conscripted population. That way the conscripted corps serve as the anvil in any engagement, tying down armies while the legions become the hammer as a mobile strike force.
On a side note, I imagine Demacians to employ holy/healing clerics.
Demacia We know Demacia recruits and trains operatives (based on Lux's judgement so unsure if still canon) that's similar to the StarCraft Ghost Program. We know they use knights, have an absolute monarchy with supporting noble houses. However, the current Lightshield Dynasty has been around only for about a century while Demacia and Noxus have been warring for thousands of years. So it's possible that the monarchy is unstable (due to battlefield losses like King Jarvan I?). We know Demacians use knights and have a thing for skin-suits.
I imagine the Demacian Army to be like North Korea... kind of. Fanatical, highly-trained (though if effectively-trained is a different story), and capable of immense numerical superiority if demanded. But the cream of their military focuses on their knights which is their standing army. There's most likely a lot of customs associated with these knights, similar to Fiora's dueling thingy, that hasn't been explored yet.
I also expect them to have a secret necromancy corps.
Zaun Private armies of various strengths and specialties. Like... you want bear cavalry? They got that. You want dragons? Got that. You want women in scantily clad outfits riding motocycles and jousting with lances? Well for the right price...
Piltover I suspect they might not even have a "army". They might be similar to Japan, being the City of Progress, and maintain only a Self-Defense Force or Law Enforcement. They have zeppelins, so an air brigade with jump/jet-packs and para-troopers is not out of the question.
Bilgewater Pirates and booty with the best navy in the world if properly paid for.
Shadow Isles Northrend
Ionia I think Ionia is interesting because my headcanon gives me an image that it's rather decentralized. There are various schools of disciplines and martial arts with each having its own students. If you've seen Ip Man or any other martial art film set in modern era, it's basically a bunch of rival gangs essentially. So while the total sum of Ionian's military could easily rival or even surpass that of any other, they lack unity due to the sheer number different schools and competing headmasters jockeying for more power.
Freljord Low-tech. Also shamans?