Since Auto Shot uses no Mana at all, it is the most "efficient" shot from that standpoint, but it also does not extra damage (except for crits). The next most efficient shot is the Steady Shot. For the extra damage it does it uses little Mana, and therefore should be the "go to" shot for extra damage. Stings, Arcane Shot and Multi shots use too much Mana, and should be used as Kill shots if you still have Mana left over at the end of a fight.
Here is my Shot Rotation Macro:
#showtooltip Steady Shot
/cast !Auto Shot
/castrandom [target=pettarget, exists] Kill Command
/cast Steady Shot
Line 1 of this macro simply replaces the "?" icon with the Steady Shot icon once I put it on one of may Action Bars.
Line 2 is a little less obvious. Clearly it is intended to get Auto Shot started so we get one shot in before the cast for the Steady Shot. But what is the "!" for? If you look at your main Action Bar (as long as you have not changed it) you will see "Auto Shot". If you click this, it starts the Auto Shot, and your character will shoot until it cannot any more. If you click it again, the character will stop shooting. So this button is more of a toggle than a cast. What the "!" does is make sure you are only starting the Auto Shot, and not toggling it. This is very important, as you do not want to lose damage output by turning off your shots!
Line 3 will attempt to cast the Kill Command spell, which gives your pet extra damage on the next hit. Kill Command is only available after a Critical Hit, and can only be cast once the cool down is over. So this is simply a spam of the Kill Command, but it will only be cast if the pet has a target (and not in "Stay" mode). If the cool down is still in effect, or no crit has made the spell available, there will be an error message (more on this below).
Line 4 will cast the Steady Shot, which was the whole point of the rotation.
Line 5 clears the error messages from the screen, which is important when battling! You will still here verbal messages from your character if you have that turned on.