It is better to leave the bowl on if you plan on cooking for a long time or if you want to fill it and bake it in the oven. The mushrooms will become firmer and their structure will remain when they are done cooked.
Do you prefer to eat them raw? In this case it is better to peel them, so they are more pleasant to eat.
If you want to get the beautiful white or brownish color (depending on the selected variety), clean it with a soft brush or a special mushroom brush.