My unit "when I attack" triggers, then the priority goes to the owner of the next pending item on the chain, that is me, right?

Not quite — it depends on whether the opponent also has "when I defend" triggers.

Here's how the initial combat chain works (Rule 464.2.e):

1. Attack triggers (your "when I attack") go on the chain first.
2. Defend triggers (opponent's "when I defend") go on the chain second — on top of yours.

After all pending triggers are finalized, the controller of the topmost (newest) chain item gets priority first (Rule 337.4). Since defend triggers were added last, that's the defender, not you (FAQ #4513, FAQ #6641).

If there are no defend triggers at all, then yes — your attack triggers are the only items on the chain, so you get priority as their controller.

But if the opponent has even one "when I defend" trigger, it sits on top of yours, and they go first.