Thanks everyone. As it says in my signature, I'm very germophobic. So I was wrestling with how to proceed. At first, we got a few eggs that had some ick on them due to being laid on the coop floor and getting stepped on. So I washed them but after I did, all I could think about was that poop water splashing over my sink and maybe (horrors!) on my countertop or myself. So I decided I would wipe off any visible poo and then wash, so no solids would be splashing about. So the next time, right before using, I wiped them off (clean ones) with a wet paper towel and then thought maybe I'm being too nervous and just used them without washing. I'm still among the living, btw. So I thought maybe a quick poll here would help me to not worry. I think I will just wipe any poo off with a dry cloth before storing and not worry about washing at all, or wipe and then wash only the poopy ones and refrigerate. The funny thing is that 20 or so years ago (when I was sane) I raised laying hens and thought nothing of just putting poopy eggs right in my fridge (in the built in egg holes) and would eventually wash them but put them right back in those poopy egg holes. And I'm pretty sure I never washed my hands after cracking eggs, plus I made noodles back then so I had my hands and counters covered in egg noodle dough. Somehow I lived. (I didn't have kids or a husband back then-only a deadbeat boyfriend who also still lives-I think).
As for now, we don't refrigerate so far. I probably will once we have a dozen, because I have more fridge space than counter space right now.