The small moving boxes from Public Storage, U-Haul, etc are the perfect size to store and/or ship records. Cost is about $1.50 per box and will hold about 110 records. If you plan to store records for a long time, you may want to cut pieces of 1/4" or 3/8" plywood to LP jacket size and place inside either end of the box to keep it from bowing out. If you are going to ship, put an extra layer of cardboard on the bottom.
Jim