Cleaned on the Loricraft , then a new mofi inner sleeve and finally the thickest quality outer available. I like those thick outer sleeves because they are very clear and never yellow and when stored properly upright not packed tightly the jackets are kept protected and they fit doubles very well and slide easily.
I never reuse used/original paper inner, as paper is a food product for mold and bacteria so why put that back near a cleaned record when I don't know its storage history. If they are originals with information or design printed on them and not just generic I will keep them in separate outer sleeves (as well as any pics, decals or posters), so should I sell or trade they are available to the buyer.