As you say, a lot of this depends on the way particular games work. I found that I got a lot of mileage out of play acting in Marvel Heroic Roleplaying because people already understood the broad outlines of the character, which meant the particulars I was bringing to it could be understood in the context, my jokes would land better, etc. But in a game like DITV it pays to have a sketchy character and get invested as you go depending on which aspects of the situation in the towns resonate with you and seem like something your character ought to care about.