Great call on using Firefly as a model--that's exactly how the campaign was sold to us!
Firefly is the show that has launched a thousand imitations, and as one of its biggest advocates, I agree that it was the best written science fiction TV show of our generation. But while a lot of the core ideas of firefly could be used in an RPG, if you tried to directly port Firefly to a table you would be horribly disappointed.
RPGs are supposed to be inherently social activities, and one thing that I've learned that I didn't understand when I was 20 and which I hear very little talked about in the industry, as what is functional for an RPG both in themes to explore and type of play depends heavily on the number of players you have. If you're looking afield for source material to base your RPG on, you need to consider ideas like:
a) Is the original source material largely the narrative of a single protagonist (Private Eye fiction, John Carter, Conan, for example) with occasional side kicks? Then it's probably suitable only for 1-2 PC's unless you radically change the style and focus of play from the source material.
b) Is the original source material feature The One, The Chosen, The Messiah, The One Gizmo, The End of the World, or other persons of destiny (Avatar, Dune, even to some extent The Lord of the Rings and Star Wars)? If so, you're probably going to have to invent new secondary lore and a new style of story that differs from the things that inspired you.
c) Even if it is an ensemble cast with a set of protagonists, do those protagonists tend to go off on separate concerns and solve problems individually? If most scenes don't involve most of the protagonists being on screen at the same time, working on the same problem together, then it's probably not as easy to adapt to play as you might think. Or it might be limited to being more suited to a smaller group than you might think. Star Trek for example when you boil it down, ToS had only 3 Player Characters (Kirk, Spock, and Bones). Everyone else only got enough screen time to be an NPC henchmen. TNG arguably had ZERO PC's, as most stories tended to be single focus/single perspective with a rotating cast of protagonists (This is a Picard story. This is a Data story. This is a Troi story. This is a Riker story.). Firefly has a great cast of well-written characters each having their own competencies, but most of them in RPG terms are NPCs. The Captain is a PC, and it's possible that Zoe and Jayne are PC's because they tend to work together, but really only Malcolm is involved in the whole story of Serenity.
Your story has to involve an ensemble cast that works together where no one is more special than anyone else, or its not really a social RPG.
Thinking further about Firefly, it's even harder than that because the story of Firefly is these people living together, but what carries that story is mostly a series of low melodrama scenes where two characters share a private moment together (very similar to another great Sci-Fi TV show, Babylon 5). Capturing the spirit of that in a table top RPG might be next to impossible, because from a table top perspective that involves a lot of people going off into separate rooms and doing their own thing, or else most player's acting as an audience and taking enjoyment from sitting around watching people create drama without necessarily this being their scene.