I keep it in the original bag
While I don't get into roll paper often, there are two rolls 12" x what started as 275' in my freezer at the moment.
I openned the original brown craft paper and plastic bags, cut what is needed, and then re-sealed the bag by rolling it shut, and then using about 5 strong foldback spring clips to hold the folds shut. It is not perfectlt moisure proof, but it work alright.
I have also stored a 5" roll in an old 11x14 enlarging paper envelope, that was folded and taped shut. I never thrfow out old paper envelopes; they always become useful at some point in the future.
I tend to cut ahead of time an assortment of sizes, because cutting off of the roll is such a chore.