I don't think you will get one right answer, you will have to decide how you want to do it, I always wash my eggs under hot water, only scrubbing any poop spots, than I refrigerate. If I don't scrub the bloom remains mostly intact. Good luck choosing what's best for you.
I have always read it's bad to leave them out on the counter, but many do it, personally I think it's a bad idea, and eggs last longer in the fridge. Always cook your eggs well, wash your hands after handling birds and don't kiss chickens, and enjoy.