I refrigerate in a low humidity drawer
I don't refrigerate. I think that the best general advice is just "cool, dark place with some air flow." If you have the space in your refrigerator, then go ahead and use it. But if you don't or, like me, just don't prefer to refrigerate so many things, don't worry. I don't feel I have any problem with sprouting or other loss of quality.
I keep them in a bowl on the counter and they seem to keep very well, for quite a while. However, I just bought some that are half the size of what I've been getting, so they may not keep as well, and since it's March instead of summer or fall, they may have been stored and feeling ready to sprout. Basically, I treat them like onions.
I keep them in a bowl in the back of my pantry where I store my garlic and onions. I've never had a problem with them keeping or sprouting.
I use cheese cloth, tie the top and hang from a cabinet knob. I use them up very fast & my cats don't notice them, God help them if I catch them on a countertop!
They keep a long time if you store them like onions or garlic. I keep mine in a bottom cabinet drawer.