Most people that ship hatching eggs, use some sort of double boxing method. They either wrap the egg in bubble wrap and place it in a small box with lots of packing so the eggs cant move. Then place that box in a larger one and put extra packing around the first box. Some use Egg Cartons for the first box.
Eggs that are shipped don't do as well hatching as one from your own yard. 50% on fertile eggs is what can be expected. I have had some people report 70% on my eggs. I have also gotten 60+ % on shipped eggs using a broody hen. Eggs should be kept between 50-60 degrees for optimum hatch rate. I have had eggs hatch that have gotten colder than that. Usually they do well in the winter if they are wrapped in Bubble Wrap it acts as a good insulator. You do best if you pick the box up from the post office directly so they don't ride around in a cold car or truck for a good part of the day, especially in the colder northern climate.
Many people prefer to hatch out their own chicks because it is hard to get the quality many want from the hatcheries and they require a minimum of 25 chicks. Even Ideal that lets you order fewer, sends body warmer chicks with your order. If you don't want that many chickens then hatching your own is the best way to go.