As a general guideline, melee use the limit break on bosses once it becomes available. There are exceptions for mechanics, like you want an AOE limit break for the stone golem adds in Hashmal, and you want to leave the LB 3 available for healers in new content.

For general dungeons, as a melee I try to use the LB 2 if it's available when the boss hits about 15% health remaining, so as not to waste any of the damage. If it's only one bar, I'll generally use it at about 5% health remaining. Mostly because I don't want using the limit break to cause me to lose job buffs, but do want to get the maximum damage from the hit as possible.

When it comes to other party content, the priority on single targets should be melee > caster > ranged as the caster LB does more damage to a single target than does the BRD/MCH. So the ranged physical should be used for cases you need an AOE LB and have no caster, or times when the caster LB circle isn't large enough, and the enemies are in a line, like the stone golems in Ridorana before the fight against Construct 7. They're already in a line, and a caster LB can't hit a whole group.