Packing is a major milestone in any moving adventure. You can do it yourself and save money, or you can hire professionals to pack all your stuff for you. That's what they do and, chances are, they do it well.
If you decide to do your own packing or partial packing, remember that the moving company is not liable for damage to boxes packed by the customer. However, if there is obvious exterior damage on packing up your goods, make a note on the inventory sheet of your shipment.
The driver has the right to refuse to accept any carton that may be improperly packed. If the driver has to re-pack cartons that the customer has packed, additional charges will apply.
If you decide to do your own packing, get packing supplies and start collecting strong boxes suitable for moving. Complete all packing by moving day. You will be busy enough on moving day to have to worry about packing.