To get a story like this going where you're after a specific feel, probably the best advice would be using a trick from the West End Games version of Star Wars. Take a scenario, toss the characters into the action right off the bat and give them their first line or two along with some description to kind of flesh out what's going on. Have to use your head a bit with what you're setting them up for. But if you need, for example, someone to start a bar fight or have otherwise made some sort of mistake to get the ball rolling, you can just offer a fate point to whoever wants to volunteer to help and use one of their Aspects for ideas on how to get them involved. Also kind of helps with party cohesion due to the whole "we're all on the same side... because everyone else is shooting at us" thing if your story is setup that way.
Just mentioning this because a number of the Firefly storylines could be described as one or more characters making a mistake or having some past issue stalk them down and the whole crew getting involved in the mess. This of course doesn't work unless characters like Jayne are uncommon. Your rag-tag bunch has to predominantly be composed of people who have qualities that bind them to the group or a storyline like this will shred your game. Of course if you have a group that doesn't have any cohesion you're not going to be able to tell stories like Firefly in the first place although you could still use the setting.