Because I always have more jars than proper boxes to store them in, I like to protect my jars by slipping cut pieces of cardboard between them. I also place an extra layer of cardboard at the tops and bottoms of the boxes as well.
I store the clean empty jars upside down in the boxes to prevent dust, spiders, and other whatchamacallits from settling into the jars, especially if the boxes are stored in an outbuilding. This saves a little time when I clean the jars again before canning.
I don’t like to store the sealing lids directly on top of the jars because over time, the rubber will sometimes acquire a permanent indentation in them. And thinking out loud here, those indentations may result in a weaker seal? So, out of an abundance of caution, I store the lids and bands in a climate-controlled environment to prevent degradation of the rubber seals and to keep the bands rust-free.