Boxes:

moving boxes:  "moving" boxes are best shipped on a wood pallets (example here).  They are generally not appropriate for UPS, 
Fed Ex or US Postal service shipments as they will be sent down conveyors and for insurance purposes will be held to a 
"three foot drop" standard.  

IF YOU ARE USING MOVING BOXES - YOUR BOXES SHOULD BE PALLETIZED FOR TRANSPORT BY FREIGHT TRUCK.  

U-Haul, Penske and many storage facilities carry low cost moving boxes.  If you want to order online with free delivery, this site has some great rates:  
shipping boxes:  50% stronger than moving boxes, shipping boxes are more expensive, than "moving" boxes but better at protecting contents without palletizing.  Palletizing is always better (safer for the goods), than non-palletized shipments.  You can find shipping boxes, locally at most parcel shipping stores, UPS Stores and Fed Ex Office Centers.  You can also order online: