Avoid using newspaper as the ink can transfer and stain onto some items. Consider using plain wrapping paper or butcher’s paper which can be purchased from all good packing material shops.
Bubble Wrap is necessary for all electrical or computer supplies and for any breakables.
Always buy plenty of tape as you will need to secure both tops and bottoms of boxes.
Fill boxes but not so you have to squash the tops down. If there is space left in the box, fill with towels or clothing to prevent damage to items shifting around in the box.
Mattress Covers and Sofa covers can be purchased for protection. A canvas tarp or sheet can also be used.
Finally it helps if you keep an inventory of what you have stored. This not only helps with staying organised but it is important for insurance purposes.
If you are not sure how long you will need storage, go for the worst scenario and pack correctly for that period of time. If you will need access regularly try and pack those boxes near the front clearly marked.