Boxes are good. Printing companies are a good source of same-sized boxes. Or, if you know somebody whose company has a lot of printing done, ask that person for the empties. Liquor stores are another good source of boxes. With two or three of these boxes, you can clean out a cupboard in 10 minutes.
Protective paper is another issue.
I always used to use newspapers to wrap dishes and other breakables. Newspapers are plentiful and the price is right, but I always wound up washing every dish I owned, because they'd all be smudged with ink. Now I use plain white tissue paper, the kind you'd find in a shirt box or a gift bag. You can generally find it in the gift wrap section for as low as 20 sheets for a dollar. Whenever possible, put heavy things in small boxes.