I don't wash unless they're dirty/poopy/muddy (gotta love free range chickens). If they are clean and pretty, I put them in a ceramic chicken bowl on my counter, unwashed. If they're dirty I wash them and stick them in the fridge.
I like to leave them unwashed and unrefrigerated in case I get a broody trying to sit on golfballs or something
I have only been getting eggs for two weeks but I haven't had to even wipe my eggs off. Each morning, I clean out any droppings and add new shavings if needed and my eggs are very clean. If one was dirty and needed to be washed, I would wash it and use it ASAP..
I wash everyone of mine, then I put them in the frige to sell. They are use within a week at my house and my customers get fresh eggs every week. Mine don't sit around for very long....lol