A mop and bucket are cheap and simple, but a damp mop head sealed away for a move is one of the fastest ways to get a sour smell. Dry it out and bag it separately and there is nothing else to it.
Pro tip: Keep the mop and bucket accessible until the last hour, since a quick floor wipe-down right before you leave the old place is easier with the mop still in hand.
Watch out: Never pack a wet or even damp mop head in a sealed bag for a long move; the trapped moisture turns musty and can mold within a day or two.