Risus Core Rules
Inappropriate Cliches: see Unexpected Cliches
Teaming Up: is a large part of the Firefly genre - so is encouraged. Do to the suggested use of Deadly Combat for firearms, it is somewhat different and governed by the rules set in the Risus Companion (that is not required for play).
Conflicts That Aren't Combat: A single gunshot is usually enough to bring the most stalwart adversary to his knees and end the fight and is considered Deadly. Any conflict engaged in with firearms usually starts as a conflict that isn't combat. If the loser manages to 'combat' his wound in a single-action conflict he may continue. This may mean traditional combat or another single-action conflict at the GM's discretion.
Character Advancement: As written.

Risus Advanced Options
Hooks and Tales: As written.
Pumping Cliches: As written.
Double-Pumps: As written with the caveat that it is only for Telepathy, a VERY Rare occurrence in the 'Verse' and requires GM approval.
Funky Dice: Not necessary for the setting, but could be reached through advancement as usual.

Risus Companion Appropriate Options
Lucky Shots & Question Dice: As written
Sidekicks and Shield-Mates: As written, used for ship improvements.
Deadly Combat: Strongly recommended for encounters that involve firearms.

Risus Options on this Site that are Appropriate
Bouncing Off the Walls
Degrees of Success - Bring the Heat!
Out Numbered and Out Classed
Ranged Attacks