Call around to all the movers and ask if they have used materials at a discount price. If you still can not flnd a real deal go to your local recyler.
Larger institutions receive supplies in boxes every day (i.e. hospitals) and the sizes are much better and more useful than liquor store boxes.
The better boxes you pack with the quicker your movers can move them.
Closed top boxes are important because they can be piled safely and dollied where ever possible to save time.
A link to a super source of packing materials is the U-haul website.
This site provides a secure shopping cart program that lets the user chose and order materials for delivery to your home.
Common materials and a guide fair prices