How does Targeting Priority work?

A ship will evaluate all the possible targets it has in its current range. Out of those targets, the one that matches the priority list the best will be selected as the ship's target. I'm under the impression that it does this check for each weapon it has.

The target type list will determine the ship's movement priority - ie which targets to engage.

Space Empires Depot | SE:V Balance Mod

I had thought the list was prioritized (or in other words, it will attack what fits the top item of the list first, then what fits the second item, and so on). Each unit (fleet, task force, or ship) makes the evaluation everytime a target enters weapons range.

The ship will maneuver against the enemy that conforms to the highest priority.

If the target ship is out of weapon range, the weapons will still fire at other targets which are in range. I haven't watched to see if these secondary targets are also prioritized.