This is just a list I made because I really can't wait to get more lore and skins for the SG universe. Also, I may or may not be in the process of brainstorming a story about the two star guardian teams and their adventures.
Starlight Manipulation: We'll start with the most confusing thing in this universe. So, The First Star (which is the sentient creator of life in the universe) gives a portion of its power to worthy, courageous individuals with light in their hearts. When they get their power, their inner Starlight (which all beings have. Sort of like their soul) is awakened and they're supposed to use their abilities to fight off the alien/void creatures that threaten all of Earth or Runeterra or Japan or wherever the guardians live (and possibly across their own section of the universe as well). They're kind of like Green Lanterns mixed with Aspects like Zoe and Leona. This power from the First Star augments their natural characteristics, giving them cool magic powers of all varieties.
TL;DR: It's an excuse for them to have their in-game abilities.
Flight: All the Star Guardians we know of can fly, even between planets.
Environmental Adaptation: They can travel through the vacuum of space, survive on other planets, survive entering the atmosphere of planets they visit and flying so high in the sky that there's little to no oxygen.
Enhanced Durability: They have to have some kind of resistance to be able to survive falls, alien attacks and anime fight injuries.
Familiar/Weapon Creation: Something they need (Soraka) or an aspect of their personality or purpose (everyone else) manifests in the form of an animal companion or weapon, or an animal that turns into a weapon. Most guardians prefer one over the other. Maybe it's because the companionship isn't as important to them, or maybe it's because they don't want to have to search around their bedroom for their weapons when Krypton is about to be destroyed. They can send their familiars to do scouting or spying (like Syndra and Ezreal do) and the familiars can access some of their guardian's powers (like Pix and Zephyr).
Costume Generation: They can magically suit up, similarly to Sailor Moon, the Winx Club, Miraculous Ladybug and stuff.
Powers
Need for Secrecy: Star Guardians have to keep their identities secret and they're encouraged to adapt to the customs of the world they inhabit. They likely don't have to keep the work they do a secret since I doubt killing void creatures can be done without notice for long, but they can't go around saying, "I'm Luxanna Crowngard and I kill Queen Beryl/the Frozen Watchers' minions!" My only issue is the world they inhabit part. Urgot The First Star chooses regular people to give power, so do they have parents? Does Lux still have a brother? Did Miss Fortune's mom still die? Because Lux's team has their own apartment and they're either high schoolers or college students. And since Ahri's team is "from the outer cosmos" are they all from another world or did the deaths of Ahri and Miss Fortune's teammates result in their section of the galaxy being overrun by the Void and force them to come to Lux's world where The First Star created two more guardians? How do foods taste purple to Lulu? When will Urgot get a Star Guardian skin?!
Trauma: Here's life as a SG in a nutshell. You get cool powers, a magic pet and the ability to travel the universe. The only con is the constant battles where you're destined to watch your teammates be killed by Voidborn, then move on from team to team to repeat the process until it's finally time for you to die yourself. That's pretty traumatic, so most veteran Star Guardians have some kind of depression or anger from it.
Dependence On Their Bond As Sisters: They fight as one or fall as many. So if they don't all stand up against a threat and work together, they'll eventually end up losing to it. I guess The First Star really wants them to be close friends. An explanation for this could be that Urgot The First Star gave them just enough power to beat their threats and losing a member would be like fighting at 4/5ths of their full power OR that it's like Charmed, where when there's discord in a collective group, all their powers are weakened.
Destiny: Star Guardians are destined to fade as brightly as they burn. So basically the more impressive and powerful they are, the worse their demise will be. Whether it be because they sacrifice their lives or get outnumbered, The First Star guarantees they will die horribly after fighting its battles.
Rejecting their Destiny: It's rare but they can reject their destiny. I don't know if it can be done at any time or if there's a certain window of time they have after first getting their powers, but the act would "reverberate across the universe and beyond" which doesn't sound good.