Totes on shelves in the basement. One is nothing but drywall tools and supplies. The OP didn't say what his situation was, but I'm coming from the perspective of someone who does drywall maybe once every 3 years. Same for painting supplies (brushes, rollers, drop cloths, etc.) and other homeowner stuff.
I think the best answer really depends on how often you do drywall but I can't think of any reason to keep them in a roller.