Most movers offer packing services. A few experienced movers working together can get your entire apartment packed in a matter of hours, which is significantly less than the days it would take you. Obviously, an entire house takes longer to get packed, but the time you save grows is well worth the cost.
You may still want to be involved in packing, even when you have a knowledgeable packing service. They may suggest a great system for color coding or labeling boxes, but it will only work if you are there to tell them what's really important. Even when dealing with movers with an impeccable reputation, your peace of mind will be greater if you take care of your jewelry and papers that have important personal information on them yourself.
Your movers should make a point of packing a couple of boxes with things that you will need immediately in your new home. Be even more practical and pack them by room, and then make sure that you label them clearly. When you move in, just unpack "Bedroom 1," "Kitchen 1," "Bathroom 1," and so on. You'll be ready for your first night, probably in an hour or so, which will make you feel better about things right away.
Sometimes, too, we tend towards overkill when packing something we think of as breakable. Professional movers know what needs to be done to keep china or glass safe, and they won't pack it in so much extra material that you have thirty more boxes than you really need.