While you are waiting six months or so for an oil painting to dry before you can varnish it, it needs it to be out of the way and protected from spatters or collecting dust. Even if it is touch dry already, covering tightly in plastic will stop it from receiving the oxygen it needs to finish drying, any paper laid on it will usually end up stuck to it and bubble wrap can leave an impression of its pattern on the surface.

If you have just a few paintings you can store them flat on a shelf in a closed cupboard or in the gap across the tops of books in a bookshelf, or vertically in a homemade divider or something similar to a letter rack or vinyl record rack or if they are large simply tilted face to the wall on the floor (usually elevated on blocks to prevent the lower part collecting dust blowing around on the floor. Many painters have developed a version of a sort of tower of drying space using a stack of gator boards or other thin, rigid panels, separated by four objects, one in each corner, such as large canvas wedges, water bottle caps, small yoghurt cups or similar, just as long as all four corners are the same and tall enough to lift the next board above the surface of each painting.