A LEGO collection is part building set, part loose parts, and the two need very different handling. Photograph built models, bag loose pieces by set, and nothing ends up as an unsolvable pile of bricks at the new house.
Pro tip: If you still have the original set boxes, use them; they are sized exactly for the pieces and make identifying a set at a glance effortless.
Watch out: Never pack loose LEGO pieces in the bottom of a box under heavier items; even small crushing force can snap thin pieces or bend baseplates.