Limit Break Caster or DPS First or Last Boss

[Squintina]

Who?
Single target? -> Melee LB
Multiple targets? -> Ranged or Caster LB (most likely Caster).
Melee LB is more potent than ranged/caster LB because the other ones are aoe (line aoe for ranged, normal aoe for caster).

Shit reaaaallly about to hit the fan because over half of your party's dead? -> Healer LB3
People in party don't seem to know how to do mechs or dodge and are overrunning the healers and something big's coming up -> Tank LB3 (dat shield)

First/Last boss
The most typical one is Last boss.
But sometimes groups will want to use LB1 for first boss, because the rest of the instance will have enough time to gather up the rest of the LB bar for the last boss as well.

Other things of note
More LB is generated if you have unique jobs/classes

Healers get more LB generation for healing people with critical health

You don't have to think "well...melee LB is better but our melee has bad stats so maybe the ranged would be better". No. None of that.
The base potency is based on the role, while the potency multiplier is based on the entire party's ilvl. There are no damage buffs, no damage debuffs, etc..