Not to ruin the magic for you, but there's a pretty clear inspiration for the storyline.
The companies aren't working together because they have similar goals or values, they're working together because it's the only chance for Eorzea's survival.
Presently, each company is dealing with its own internal strife and accusing the other companies of sitting around, twiddling their thumbs over pettier things, while the world goes to Hells in handbaskets. Each thinks that they are the only company that can see their people through the Umbral Era while the other two cannot be fully trusted.
This is why you should choose the company whose leader struck you as most charismatic, whose goals and reasoning you resonated best with. Invariably, all three companies will face challenges and succeed in the end, but how and why they win against the Garleans will be entirely different, and they'll be happy about it and proud of it from different angles. If you choose a company that has values or strategies you don't resonate with, the whole story will be all the more shallow for it. The three-city-system exists to give the best chance for everyone to find a story they find meaningful and powerful. Try to tell me that there wasn't one storyline in FFXI that stood out miles above the others... Now, after you all nod and agree that there was, turn to eachother and say aloud which it was. Aaaaaand flamewar!
I really need to just dedicate myself to the writing the lore instead of playing the game.