If there's more than one type of counter on the targeted permanent or opponent, Etched Slith's controller chooses which counter to remove.

In a case where you put more than one +1/+1 counter on Etched Slith with its last ability (for example, because of the effect of Doubling Season), the reflexive ability will trigger once for each +1/+1 counter you put on it this way.

You don't choose a target for Etched Slith's last ability at the time it triggers. Rather, a second "reflexive" ability triggers when you put a +1/+1 counter on Etched Slith this way. You choose a target for that ability as it goes on the stack. Each player may respond to this triggered ability as normal.