Skyship Plunderer's triggered ability gives only one counter of each kind. It doesn't double the number of each kind of counter. For example, if a creature has two +1/+1 counters and a charge counter on it, it gets one +1/+1 counter and one charge counter.

To give a counter is to put a counter on a permanent or to have a player get a counter. Effects that interact with a player getting counters or counters being placed on permanents interact with Skyship Plunderer's triggered ability.

Skyship Plunderer's triggered ability can target any permanent or player, regardless of which player was dealt combat damage.