Packing is one of the most important aspects of your move. It is recommended that you have the proper moving boxes. The ones you can get from supermarkets may be free but they're not nearly as strong or padded. They are more susceptible to causing damage to your valuables in transit.
Always remember that the heavier the item, the smaller the box that it should occupy. Buffer and separate fragile objects with sheets, blankets, pillows and towels. Fill in empty spaces to minimize movement during transit. Always mark the boxes containing fragile items.