Regarding what I wrote above:
My interpretation was wrong, because it would not allow Reactions to behave as expected. This means the rules for what "when you play" means are a bit more complex than I thought. In any case, it means the following:
I was wrong in my possible interpretation regarding Champion (before the new ruling) not triggering on its own playing. All "after" abilities (like Citadel) trigger after the played card is resolved, not before. So Champion needs to be "first" in order to not give you an extra Action when you play it.
The conclusion is that Champion happens "first" (and will apparently say that in new printings), while Sauna and Merchant still happen after.