I use a 2" cardboard roll core, rolled up with a long, piece of waste inkjet canvas. The canvas is attached to the tube with masking tape. I never use the last couple feet up near the tape attachment, that avoids getting impressions from the bump made by the end of the roll. One advantage of cardboard/canvas is that it generates zero static charge. The canvas lays super flat which is a nice feature in this application, one only has to deal with the curly print. Some fine art paper on the soft side might do as well, or even butcher paper from a cheap roll bought at Michael's hobby store.
I think the most effective diameter is just a bit over 2 inches/ 50mm for most media.