I’d get them in plastic, and try to cut the top side of the bag all open within a few days, and often I get through them all without problems but sometimes not.
I do now have a plastic container I could dump them in that could be an improvement. I’ve thought of cardboard boxes but I imagine spores getting into the cardboard for the next potatoes and maybe moisture from the potatoes being a problem.
My mother kept potatoes in a plastic container in a cabinet, but I don’t know how well they kept or how quickly we used them up.
How did they store them? The only cellar I’ve ever been in was of the house we lived in when I was a little kid, and I remember it as so wet and filled with spiders, and maybe the average cellar isn’t quite like that.