Neat idea!
I've considered this myself. I think FATE could be moulded for many, if not most, settings; providing you're happy to make sure narrative takes a forefront. If you're looking for a more rulesy system there is a Serenity/Firefly based RPG already.
That said, I hope none of y'all mind if I chip in with a few aspect ideas.
Mal:
* Things Don't Go Smooth
* The Captain
* You're Part of My Crew
* What you plan and what happens ain't ever been similar.
* Loves Inara
* Aim to Misbehave
* Big Damn Hero
* On The Loosing Side, Not The Wrong One (He needs something signifying his former Browncoat status)
* Man of Honour in a Den of Thieves
* Fall Of All Seven / I'd Have To Go With Wrath
Inara:
* Companion
* High Class Lady
* Damn it Mal
* It's Frustrating to Love Mal
* Serenity's Unofficial Ambassador
* You Don't Play a Player
Kaylee:
* Intuitive Mechanic
* Innocent Criminal
* Pines for Simon
* No power in the Verse can stop me
* machines just got workings, and they talk to me
* Bright an' Shiny Cap'n
Book:
* Walking the World for a Spell
* Mysterious Past
* The Bible is Somewhat Fuzzier on the Subject of Kneecaps
* The Special Hell!
* HAIR!
* Faith Fixes You
* Shepherd's a Purely Figurative Title
* Wasn't Born a Shepherd
Jayne:
* Vera, My Favorite Gun
* As Loyal as my Paycheck
* Money makes me stupid
* Paid for "Public Relations"
* Like To Have My Options Open
* Strong as a Hammer, Crude as One Too
* The Chain of Command's What I Beat You With
* 'Can't do Somethin' Smart, do Somethin' Right
* If I'd Wanted Schooling, I'd Have Gone to School
Simon:
* Child Prodigy
* The Doctor
* Focused on Helping My Mei-Mei
* Moonlighting as a Criminal Mastermind
* Not Weak, and Thats Not Nothin'
* Rich Kid That Gave Up Everything
River:
* Child Prodigy
* They Messed with My Brain
* Empathic Mindreader
* I Can Kill You With My Brain
* They Made Me a Weapon
* I make prodigies look like idiot childs
* No Power In The 'Verse Can Stop Me (She deserves it too!)
* Two by Two... Hands of Blue
* Albatross was a Ship's Good Luck
Wash:
* Leaf on the Wind
* The Funny One
* Married to Zoe
* Oh God, Oh God, We're All Going to Die!
Zoe:
* Warrior Woman
* I Follow the Captain's Orders
* Married to Wash
Okay, most of my suggestions are quotes, or derived from quotes, from the show. Can't promise they're exact, its been a while. The rest are just ones that seem to fit, or sum up something I couldn't think of a quote for. Not all are worth using, and even if they were there isn't enough room for them. But better too many ideas, then too few. If I come up with any more, I'll let you know.