Try to use the same size box for everything, if you can; it will make loading and unloading your truck and your storage space easier. Of course, use your own discretion and test the heaviness of each box after you pack it, to make sure it will not be too heavy to lift.
Packing peanuts, bubble wrap and other packing-specific materials are great to have, but newspaper works well, too! Also, kitchen towels and pot holders can be perfect for wrapping and cushioning.
If an item you are packing has removable parts, like a kitchen mixer, wrap each part separately instead of wrapping the whole mixer together. You can put all the parts into one box.
Removing the drawers from your dresser before moving it will not only make your life easier, but the drawers can then be used as "boxes" to pack in!