Re: Why that costume
Well, The Greek wears the very same armor she first woke up in, when she awoke in the modern world (it was preserved along with her). It ties her to home, and clearly identifies her as The Greek.
Both of my characters in the Delta Defenders campaign wear street clothes, but for different reasons. Beacon does it because she's very literal and minimalist. Aya does it because she's not officially a superhero, and she doesn't want to stand out.
My only other character, Weather Girl, I haven't played in about a year and a half. She wears a clingy purple body suit, a mask and rubber-lined gloves. The mask is to protect her Secret ID. The only other reasoning behind her costume is the gloves, which protect people she touches from being zapped (she lets off a constant static charge). Otherwise, I picked it 'cause it looked cool, and I was going through a purple phase. ^ v ^