I want to know how to store eggs in the refrigerator. Some people say to never wash them, others say it's ok to wash eggs before refrigerating. Which is correct?
I would personally avoid washing the eggs.
The problem is that wet eggs are bad. This goes for both Europe, where the eggs are sold unwashed, and in the US, where the eggs are pre-washed and refrigerated.
If you did wash your eggs, you need to get them thoroughly dry afterwards. Otherwise, you will do harm to the eggs.
If you're buying unwashed eggs, you could use a dry brush on them before you stored them, but I wouldn't recommend anything more than that.
I raised chickens and handled many hundreds of eggs (my all time high was over 200 in one day.) I didn't like the idea of unwashed eggs going into the refrigerator, though they appeared quite clean.
Washing eggs does make the shells a bit more porous, so washed eggs don't stay fresh quite as long. If you do wash them, though, it's important to wash them in warm to hot water so that the contents expand slightly as they are being washed. That way, no wash water (or more importantly, bacteria in the wash water) enters the egg. Cold water would cause the contents to contract a bit allowing seepage into the egg. A quick wash/rinse with plain water is fine.
There are other ways to clean an egg, but it is far more work imo.
If you don't plan to refrigerate the eggs, you might want to just let them be, wiping off any dirt. Keeping the nesting boxes clean and good management of the coop/flock is important.