If you wish that kind of service you should deal with a formal mover. Their rates are roughly double mine. Pack boxes 30-50 pounds. When a box is full close the lid and seal it. Do not over fill them.
Large boxes are for light things.
Chests and dressers are best emptied. However it is only necessary to empty drawers if a piece is heavy. If you can not budge one end of a dresser by pressing against it with your hip please empty it. Generally drawers do not make good boxes it is best to leave them in place. If a piece is light it is OK to leave things in the drawers as long as they are not breakable or spill able.