I agree with browncpatrebels
Syntax plays a very important role in the firefly universe. or verse.
make sure your using the slang. Notice how its not "back woods hick" (no offence intended for persons who live in back woods, or who call themselves hicks) No, they use a modern stylized system of abbreviations and apostrophes. What I would do if i was you is, get the idea of your story down, like the major story arch outline finished. Maybe even get a few little minor story arcs drafted out too. Then go back and watch all the firefly episodes back to back. Have a pad and pen ready and whenever someone says anything cool, like the way any word ending in "ing" can be ended with an " 'n " instead, or how universe is "verse" or how "them" is "em" Yeah, write all that stuff down. Also write down when they talk about technical stuff. I think the writers did that on purpose, leaving out technical details, cuz they didn't have all that stuff worked out yet. But any technical technobable they use, make sure to write it down in a different section (if you think your story will make use of it)

then go back to your outline and start writing
when you get to write'n dialogue go back to your notes, or if your using a word processor program (assum'n yer not using an ole fashioned typewriter) use the "find and replace" command to replace common words with the "firefly slang"

if you do that, and watch all the episodes in a short amount of time, ide think you'd have a pretty good shot at making something which could seamlessly fit into that verse'

good luck