Moving requires a lot of equipment, and you should be familiar with each type, especially if you're planning to do everything yourself, or with family and friends, without the services of professional movers.
Wrapping Equipment
Nobody wants their furniture damaged, their glassware broken, or their ceramics cracked or chipped. For this purpose, bubble wrap is standard for any move. Buy enough bubble wrap to cover all your big items, especially furniture.
Boxes
Boxes are for moving smaller items while remaining organized. Although you could use the free boxes that you received from the supermarket or the local stores, these are not designed for heavy duty use. If you want to make sure that your boxes will provide enough cushioning and support for your possessions, buy thick, corrugated cardboard boxes.
The Big One
Your vehicle is the biggest piece of equipment you'll be using during your move. Make sure that you have one that can carry big loads. A pickup truck is ideal for this, although you will probably need to make more than one trips even with these. If you want to get everything done in a single trip, then you should hire a truck.