Have you ever noticed how sometimes when you read the newspaper, afterwards, your fingers are black from the ink?
Well packing with regular newspaper does the same thing to your household goods. While newspaper is plentiful and easy to come by, it is not suited for packing, especially for items that are light colored.
Professional movers will use plain white paper that comes in 20-40 lb. bundles ironically called "newsprint" or "news-stock". It is similar in feel to regular newspaper stock, but without the ink. My suggestion to you is to contact a local mover and see if they will GIVE you their partial/open bundles of newsprint. Once the bundles are opened, movers will generally set aside the open bundles as they are a pain to use in the future. Typically movers/packers will wrap packing tape around the bundles to re-roll them and at that point, it's easier for the mover to use a fresh bundle than to go through the hassle of getting the tape off the old.