There are many different methods of packing eggs for shipping.
Personally, I wrap each egg individually in bubblepack or the flat foam sheeting that is used under floating laminate floors. Then I put the wrapped eggs snugly in a small box and put that box inside a bigger box surrounded by packing peanuts or crumpled newspaper. My eggs nearly always arrive intact.
Some people just put a few handfuls of shavings inside an egg carton with the eggs, wrap the egg carton in bubblepack, and then pack the carton inside a box.
Ive received boxes where each egg was wrapped in tissue or paper towel, but sometimes they are broken.
Generally it is agreed that it is most important to keep the eggs from bumping into each other inside the packaging and to keep them away from the outside edges of the box where the impacts are.
Assume that the post office is going to kick the box all the way to its destination.
Putting the words Fragile or Eggs on the outside of the box doesnt help at all. Once the box is in the postal system, they dont read any of those warnings. They just read the zip code and throw the box into the proper bin or truck.
As for shipping, I sent the eggs Priority mail with return receipt requested or at least a confirmation number. Express is a waste of money when shipping anything other than a live adult bird and even then it usually arrives in two days anyway.
Chel