Last time I bought batting yardage they gave me the roll it came in & the plastic that covered it from the manufacturer which I keep in the workroom closet. Some quilters make "batting tube covers" for storing batting yardage. I have a Giant Zip Lock for smaller batting needs. I have no space on my workroom walls to mount batting as it would protrude from the wall too far.
I lay down a California King sheet when ready to cut batting for a project (sometimes two overlapping sheets for projects with hanging sides); lay down the backing, wrong side up; roll the batting onto the backing; cut what I need, using the backing as a guide; roll & re-wrap the unused batting for storage; put the quilt top on the batting, right side up; roll my project; take it to my longarm table to be basted or quilted; put the sheets in the washing machine. Some quilters use & reuse wide muslin to lay down projects & store in containers until needed.
This process seems to keep everything clean. I use my Cal King bed or the large room floor for project layouts.