Candling is important for incubating fertilized eggs. It isn't really important for selling fresh eggs unless you or the customer are uncomfortable with the idea of fertilized eggs.
Personally, I only wash those that really need it. Some eggs will have poo or other dirt/bedding stuck to them that doesn't easily come off. Those definitely need to be washed. Keeping the nest boxes clean definitely reduces that problem.
Eggs naturally have a thin, waxy coating that protects them (the "bloom") and washing rubs it off. The US requires washing for commercial eggs, but the equivalent European groups don't and they are commonly sold unwashed. Both ways work. Unwashed eggs can be kept on the counter top, but washed eggs must be refrigerated.
I always sell the cosmetically nicest eggs, so I let my customers know about this and it is up to them if they want to refrigerate or not. Of the eggs that I keep, those that I wash go into crates in my frig and unwashed ones in the spring are preserved using "water glassing" for use over the winter. Water glassing stores eggs in lime water and the waxy coating is important to keep the water from penetrating the eggs.