Everybody will have their own preference. And so long as there's no health risk, all are good options.
I personally refrigerate all my eggs, unwashed.
I expect that some will get a little dirty at times, but as long as the coop and nest boxes are kept clean and dry... the eggs should be clean most of the time.
I use dirty eggs first, preferably within a day, and might wash them right before use depending on the situation.
If there's any damage to the shell, it's an automatic toss for me. Exception is if I accidentally cracked it just then, and the cracked area hasn't been in contact with any debris or dirty surfaces. Then, I will find an immediate use for that egg since it's still safe. But I never keep eggs with a damaged shell.
So, we don't go through eggs very quickly, and things have been very busy this summer. Ended up with a lot of eggs filling the fridge (I place dates in the cartons, so I know what days those eggs are from)
Generally we try to use older eggs first, but that didn't happen this time. (*any gifted eggs are the most fresh ones, of course)
We cleared the fridge today and just processed some that went back to July!
All eggs were clean, unwashed (as I use dirty eggs immediately, and never mix washed eggs with unwashed eggs)
Most of the eggs were still good. (We float them) but, they were my pullet eggs and thus were smaller.