Paper in any form is valuable. Separately storing newspaper, magazines, cartons that are collapsed and bits of paper is ideal. Do take out the inserts from newspapers and store them with the bits of paper. Do not store greasy or soiled paper with the good paper. It reduces the value of what you will get eventually.
Paper can be recycled up to seven times, so storing every bit helps. We know this helps save trees but did you know it also saves water? Recycling 1kg of paper saves 35 liters of water, which is about 2 buckets!