I keep my rolls in plastic bags bungee cord secured. Since I have a HQ I keep the bolls flat on the floor behind my HQ. I learned not to put the roll up on end as the batting begins to slide down and distort a bit.
I don't want it stored in my garage as I want it clean and bug free.
I have a very sturdy homemade [by a friend] table for my HQ and I have a day bed without the trundle under that table. Thus the batting goes behind it all. I tend to wait til I have a few tops finished and then measure the batting for them all at the same time.