All I can help with is Horde, so I’ll write a little blurb:
Well, I’d say to try your luck at some of the more social guilds that are prominent, at least on Horde-side. The way you worded it implies that you have some fatigue with a militaristic setting, but I would say that all the military guilds the Vol’kar interacts with has far more depth than what forum posters imply. i.e. it’s not all about rank, power, honor, formations, killing, etc - anyhow.
First step is checking out the Horde directory. WrA Information & Directories (Guilds | Communities | Events)
Firebrand Enterprises and Brightmoon Faire are always good first stops.
For Alliance, I wish I could help out more, but there is no Alliance directory, and for that to happen there needs to be initiative to revive it. However (hey look Baitan just responded) checking out the various discord(s) is a good next step for networking.
Shaureyne linked it in another thread with a better explanation, since I’m not actually in that discord.