Kyon is always, and must always remain, the 'everyman' He is trivial to insert, so we'll move on. Perhaps the only issue is how to keep him the everyman and painfully mundane in a universe with so many ways to be awesome.

Koizumi is the team Esper. Psychic on the run from Psi-cops? Maybe a deep cover agent who lost the plot and has gone rouge as a good guy? He'll work as both.

Mikuru is the time traveler. It's not exactly a mainstream thing, but it DOES exist in universe. And she's from far enough in the future that she's unused to all normal technology. She's obviously here on a training mission, to acclimate herself to the current timeline so her future self can come back and do Secret Mission type stuff. Which she does!

Yuki is an alien. More to the point, even for UF she is truly an alien life form, a program designed to translate the will of a god like being that has existed since the beginning of the universe. She's also three years old. She's very good at her duties, and very bad at being a 'human'. She might have been sent to talk to galactic civilization as an ambassador, or she might be here as an unknown observer. Whatever her reasons, she's learned how to play a mean guitar solo.

Then we have Haruhi Suzumiya. I'm pretty sure she's the hardest one. After all, UF has no room for an unconscious sleeping Godhead. Moreover, in a universe with aliens, time travelers and Espers, there's little reason to go looking for them. But her real motivation is to be unique, to stand out from the crowd. To stand apart from the teaming masses, to EXCEL. Even the most elite organization will not do. So she makes her own bizarre one. A high school club to gather up the time travelers, the aliens, and the Espers and have fun with them! It is, in many ways, a mission statement for the entire universe. Maybe she isn't such a bad godhead...

“Navigare Necesse Est”-'Get me out of here!'