I washed one quilt top because it was really skanky. (It is a 1930/40s? top my MIL's grandmother made and it was stored unprotected in an old trunk.) It will take some serious ironing and squaring before I can actually complete the project. Unless you plan to wait decades to finish the project, don't worry about storing it. I sometimes just fold my tops loosely and keep it with the intended backing. I have a bunch of project tucked away on a shelf.