I only had one and then TONS of waterproof lap pads to lay on top of the changing pad. We only had to wash the changing pad cover out of the ordinary if there were to be an epic blowout that went up the back and down the legs. Typically the lap pad would just get dirty and I could wash just that.
I only have 2 because as you have mentioned I bought a couple packs of the waterproof pads. I figure they won't need to be washed as often with the pads.
Re: How many changing pad covers do I need to register for?