To protect the pots and pans you could use wrapping papers. Simply crumple them loosely so they can absorb more impact. Still to provide more protection, you should layer the cushion by adding a layer of biodegradable packing peanuts. Then when putting the pots inside you should put them in groups of 3.
Get a medium sized sturdy moving box. But before putting the largest pot of the three in, wrap it with a wrapping paper. Tape the edges on the inside of the pot. Do the same on the next pot. But before you put it in, put a layer of packing peanuts between them. Do the same for the third pot. The lids of the 3 pots should go in the same box. But they should be individually wrapped as well. This way each item in the box will be protected well. You won't have hard time finding the pots and the lids that go together. Just don't forget to seal the top of the box well too.