For totting to where they will be shot mostly sihouette type attache cases, like TC's leather 10" barrel case, TC's "Indian Blanket" silhouette case and a bunch of silhouette hard side cases from different makers. I like the hard side cases the best. They can house any length of scoped barrels mixed together (pistol, carbine or rifle) as well as frames with furniture and barrels attached.
At home I made simple wood racks for the barrels. Forty years ago when I only had factory pistol barrels small ones that fit in my safe - later hidden floor to ceiling wall racks in my shop because I had so many barrels.