Invest in some plastic totes. Watch for them to go on sale and stock up. They're easy to pack and carry, and they stack neatly for storage at your new home. When you're packing breakable items, use your dishtowels, bath towels and washcloths to wrap them instead of newspaper. As you finish a box, mark it with its destination room and a rough contents list.
Bungee cords are essential during a move.
They keep dresser drawers closed, rugs rolled and sofa beds in place. Just slip the scraps under the feet and pull it along.