I often use no orders with respect to target selection. The default selection does nice things like not shoot at drifting weaponless space hulks and fires at targets of opportunity instead of producing space jams trying to get to the “target de jour.” If I notice a sub-optimal, sub-standard result in a fight, then I add one of the orders, based on what I saw.
Retaliate – useful when the enemy has deployed a “chew toy” (such as 14 armor modules and one cruiser defense laser). This order helps your captains decide to ignore the chew toy and go after a real target. (Note, the default orders will allow gunners to notice that they are having no effect and switch targets, retaliate just makes that process faster)
Cooperative – useful when the enemy has deployed lots of ships. Causes fire to naturally focus on a few ships so that the mob can be culled a bit. Also a good order to give to a ship optimized for taking down shields. Never give this order to ships that carry disruptor bombs or other specialized weaponry of this kind.
Vulture – fun! Make enemies blow up sooner! Useful when you notice all the enemy ships have repair modules, the vulture order prevents them having time to heal. This order should be the only targeting order a ship has, and the ship should be optimized for quick DPS (the enemy in this case has little armor and no shields).
Rescue – This order, along with “protector” is among the most difficult to use effectively. Basically a ship with this order should be fast and do lots of damage. I find that it’s the right order to give a mob of fighters, since it will naturally move your floating cloud of death forward to the ships actually engaged.
I find that if I’m deploying a “one trick” fleet or a fleet of all “balanced” ships, I don’t need targeting orders. If I’m deploying a mix where each ship has a job, then I need to use the targeting orders to help each ship know what it is meant to be doing.