The first ability is a replacement effect. The choice is made as Aquamorph Entity is turned face up (or enters the battlefield); it turns face up (or enters the battlefield) as a creature of that size. It doesn't become a 0/0 and then a creature of the chosen size.

If a creature enters the battlefield as a copy of a face-up Aquamorph Entity, or a Vesuvan Shapeshifter turns face up as a copy of one, the controller of the creature entering the battlefield gets to make the choice.

If a creature that's already on the battlefield becomes a copy of a face-up Aquamorph Entity, its power and toughness become the power and toughness that were chosen for the Entity.