Thanks for reminding me!
I used to work with some guys who would build special racks for their lines to allow maximum straight lengths during storage in the basement. The most radical I've heard of is the FF firemen who hang lines in the hose tower!
Bill, who now lives in Seattle, uses those contractor size spools to wind lines onto during storage. This seems to be a good compromise to me.
RE: cleaning - I thoroughly rinse my lines before any period of storage. I typically dump the line into a tub and strip it thru a piece of cloth or paper towel, for dry lines I will then apply "Glide" once in a while.
I usually don't do anything particular for intermediate lines or the fast sink stuff for SWFF, except cleaning thoroughly. My personal pref - I don't like a slicked up line for striper fishing.