The one rule that matters practically, and it is the thing people get wrong when they move: once an egg has been refrigerated, keep it refrigerated.
A cold egg brought into a warm room condenses moisture on the shell, and moisture on a porous shell helps anything on the outside get in. So moving between systems is the risky direction, not either system on its own.
Which gives you a simple rule for where you are now:
Bought from a warm shelf, a cool cupboard is fine, and so is the fridge, as long as you then keep them there. Do not move them back and forth.
Bought chilled, fridge, always.
A few other practical bits:
Do not wash eggs at home in a country where they are sold unwashed. You would remove the coating and get the downsides of both systems. Wipe visible dirt off dry, and wash your hands after handling.
Store them away from strong smells, since shells are porous either way.
Room temperature eggs are better for baking, which is a genuine advantage of the unwashed system and why many recipes tell you to take eggs out an hour beforehand.
And the float test still works in both: an egg that floats is old.