I will actually go over and post better text for all, but for now, I will do a general one. Obviously, you're free to vary from this musing, expand, etc.
The League is one of the more open-minded and independent star nations in the galaxy. They range over quite a few planets, but with relatively low populations, typically no more than two to five billion. Their first world is an outlier at ten billion, however, and the system is fairly populated.
Although the Synthetics view them as "embarrassing liberal parents", that's kind of a misnomer if you think in terms of current politics and only a partial description for the areas in which it is similar. The League simply insists upon the right to be left the hell alone in their own life as long as it doesn't impinge too much on someone else, and considers it a universal right to every thinking species (even though some of them like the Merope push the definition of 'thinking' as far as most League citizens care.) It's basically between "Like a good neighbor, stay over there" and "As long as you aren't hurting anyone who doesn't need hurting and come together with us when it's time, we literally could not care less what you do or who you are." It is far more likely for a League citizen than an Alliance citizen to be armed simply because the hostile nature of many of their worlds means that carrying a good weapon when skimming around your lands is a pretty decent idea. They're typically quietly polite by nature, partially due to many internal and external forces pushing the "hang together or hang separately" mentality, and are reasonably honest in business by principle. Most of the people who are considered "poor" by League standards are fairly land-rich by other standards. There is definitely a frontier spirit, and a notable lack of AI except where it cannot be helped or would be practical.
Politically speaking, there's a weak central government with low taxes, but theoretical dictator-like war powers that rarely get asserted but typically do with roaring support (and even less rarely remain asserted after wartime because they're severely allergic to that much concentration of power.) As such, most of the League governing mechanisms exist merely to help out your neighbor/family over thataways and to put in just enough laws for business to go about their job of making money in a way that punishes neither failure nor success. The capital planet changes every 3 standard years by a mind-boggling process only League Free Citizens claim to understand. Some non-League people consider it something between an ongoing bet / inside joke / possibly a strange cult, and there's definitely Coalition jokes like "League citizens take so long to vote because they have to sound out every word on the paper twice" and such.
But, there is one thing that every League citizen - especially the Terran-origin ones and long-time families that still exist - remember.
Betrayal.
They remember the deathtrap worlds and the effort to clean up toxic planets while being demanded by the Corrupt Worlds to pay ridiculous taxes to fund the next fleet to halfheartedly defend the frontier. They remember who the Merope didn't take loans from, are very aware that the Alliance paid for the Synthetic and Merope attack on their worlds, absolutely refuse to accept the Alliance/Formation whitewashing of the destruction of League ships by the backstabbing Formation ships, and will not forgive the Merope for frying nearly their entire Marine Corps and a significant portion of many planetary armies when the Merope committed war crimes by blowing up the War Kai sun without allowing withdrawal of occupation forces. There's memorials on every single planet.
They might not show it much, but there's a core of anger and determination to turn the League into a serious power if sufficiently provoked, as opposed to its fleets built mainly for collective defense against hostiles, system and convoy defense against pirates, and commerce raiding if needed.
Right now, they have the philosophy of "talk softly and carry a big rocket launcher", with a fleet strength of "If you push me, I'm going to push back", and "I might not win the fight but I'm sure as hell not going to lose." There's no official ranking, because the League "states" don't particularly bother to make sure the League itself actually knows how many and what kind of ships they have, aside from legally required audits every several years, and it's been postponed a few times for "business reasons" and "If we really need to know, we can find out one way or another without all the hassle." However, it's estimated that they're in the bottom half of the powers, and their war ships are getting their teeth cut on pirates (and occasional Alliance and Merope convoy escorts) regularly to where there's a solid corps of Navy who have seen combat.
Economically, they're one of the top four powers, with League convoys all over the Galaxy due to their low insurance and high safety ratings, access to a lot of wormholes, and enough planets to have a variety of products and big markets.