Use an easy and short story line line "First Time in the Captains Chair". It will keep the games to a reasonable length and will hold new players interest and allow them to learn the game without being too complicated or boring them with long wait times.
Limit the number of players per game for the reasons listed above.
It might be worth limiting everyone to base Firefly ships as well and not using the special one off ships with special abilities and starting gear. Have those on hand or near the table so players can check them out, but stick to the basics for the game so that everyone is on equal footing.
Replace the first player token with a toy dino as suggested in the rule book. Firefly fans will appreciate the inside joke.
Encourage players to consider and start planning what they want to do on their turn during other players turns. That way they are ready to go when their turn comes around and it keeps things moving.
If players are really into the theme, encourage them to come up with stories of their crews thrillin heroics long the way (as long as it doesn't interfere or delay the game). It can really add to the atmosphere of the game to have multiple fun soties going on aobut each crews glorious victories and hilarious botched jobs.
Thanks, toy Dino was one of my first purchases. I wondered about using the starter story.