Stand; not sure I've ever sat for a game, but probably because there are rarely stools around. I'd probably fall off of them or knock them over backwards now and then if they were.
Something interesting I recently noticed on a trip to The Sanctum in Meriden CT (my first time) - I have a playing stance. Specifically, I stand on one leg (my left) and cross my right foot behind my left ankle, leaning into the machine. I'm coming back to playing after many years away, and don't think I use "the stance" in my home playing, but I immediately recognized it as familiar and a remnant from my younger playing days, when perhaps I sought to project a certain aura of coolness or casualness while playing.
The era of projecting any sort of aura is long past....but the stance remains.