Whenever a character enters play this turn, put a +1 / +1 counter on it.

So this creates a delayed trigger that goes on the chain when the character actually finishes entering play, right? They don't come with the +1/+1 already on it when they hit the table, right?

That is correct. "Whenever" is one of the words that denotes a "Triggered effect".

Hah hah, okay, yeah. :) I just recalled something about counters getting calculated before characters come into play, but that must be from their own effect or a differently worded one. Wanted to make sure.

Yeah, thats the 5(?) drop Jean Grey. She is a special case though, not the norm.

The wording you're thinking of is "enters play with," that one doesn't mark a triggered power. That's even the wording Cosmic uses, as a matter of fact, which is why Cosmic characters have their counters right away.