Put paper in a paper shredder,,,,gift wrap, newspapers, magazines
Storage boxes with sectional compartments are best. If you did not get a decent original box with the items, then its best to deliberately buy one or make one.
For small hanging Christmas baubles a clean egg carton can be ideal.
For large baubles try cardboard fruit trays (available in different sizes from mandarins to grapefruits, collect them free from the local supermarket). Just like an egg carton these have a shape that keeps the baubles apart and cushions them.
Divided boxes designed for wine or liquor bottles are also ideal for protecting your tall standing ceramic Christmas shelf ornaments like; Santas and Snowmen and Angel, collections. Shredded paper can be a good buffer to avoid breakages but don't let small items get lost in shredded paper as it can cause them to be dropped when unpacking next Christmas.
Plastic cups placed in a box and surrounded with shredded paper can be a cheap ornament container. The ornaments will be separated and cushioned from breakage, and also will be easier to retrieve next Christmas.