snappis need a loop type fabric (think of traditional terry flats) for their little claws to grip onto. You can get bamboo terry, but they are more expensive than cotton.
Cotton just doesn't hold as much liquid as bamboo. Saying that, when they are little you change them so often it's not an issue.
Generally they just sit inside a snug cover I think. So you put them on and then the cover and they don't move much.

I had Maz ones, but I sucked at them, so I'm no real help.