Crikey, what a good question.

Firstly, they should be stored fully unwound. This takes the tension off the springs thereby making the watch movement last longer.

secondly, the leather bands should be treated with a leather wax. If treated it should not matter if they are laid flat or not, just make sure the leather is treated.

To store, a dust free case is best. What that looks like is up to you whether you simply want to store or be able to view them as a whole collection. If you are simply going to store them, wrap them in a lint-free clothe first. Again this will keep the dirt and grime out of the movement.

Oops almost forgot, I hope we are talking about antique (or old) watches and these new cheap battery operated ones? If they are then just chuck 'em in a box and away you go.....