I use a pencil....I would just make sure not to use any kind of marker or oily ink (like ball point). The only reason I wouldn't use a grease pencil is it's oil based.
I've seen that others use a simpler method---they write the date on the carton (or a label on the carton) with the date of the oldest egg in the carton.
Although refridgeration is not required so long as they are kept in a cool place, most do. (europeans in general do not, and I suspect most of the rest of the world does not)
Store bought eggs can be as much as 30days old by the time they hit the shelves! So keep that in mind when your deciding what's considered old. For me it's a matter of quality. By the end of ~4weeks, I'll hard boil them, and then I'll keep 2 weeks more. They usually never get that old---our family eats lots of eggs and my neighbors and friends get them long before then! If I ever end up with "old" eggs, I scramble them up and feed it back to the chickens.
I do NOT wash my eggs as I don't want to wash the natural protective "bloom". I will sometimes take a dry scratch pad to get the dirtier parts (if you keep clean nest boxes and collect at least daily, this isn't needed often). With my ducks, however, I often need to wash them--but if I do, I use those first. Washing eggs with water warmer than the egg, keeps the "dirt/bacteria/etc" from getting "sucked" into the egg. I will wash them just before use---which is what I tell my friends and neighbors if they ask about it.
I always hard boil the oldest ones, they're way too hard to peel otherwise!
Enjoy your eggs!
Sandra