I ship eggs. I use a Flat Rate Priority box and pack the eggs in crumpled sheets of newspaper. I add a cool pack if it is hot weather. I send them Priority, shipping is either $12, or $15 with delivery confirmation. I mark the outside of the box Fragile and Perishable on every side. Some people feel better to have me write their number and ask the PO to call addressee for pickup if they have any concerns about the weather, the delivery person, or if they just want their eggs ASAP. That's about it.
It is recomended that a person wait 8-12 hours before putting them in the incubator to give the insides of the eggs time to settle before starting the devolopment process. I have done both ways, wait and put them in right away, and to be honest, I have not seen any difference.
Hatch rates usually vary from zero to 50%. 50% on shipped eggs is considered OUTSTANDING outcome. I don't spend any more on shipped eggs than I can afford to light on fire and toss down the garbage disposal, because that might be your outcome. If you are starting out with incubating you may want to find a local source of free or inexpensive eggs to practice with until you feel you have it down pat and are good at incubating. It is not an automatic success sort of a hobby. There is a difficult learning curve that goes with it. Lot of info and help here on BYC to get you started in the right direction.
If you do get good at it and are interested in any of my breeds of chickens I would be happy to ship you some when you are ready. Click on the "Website" link under my name to see some of the varieties. I really need to update because it is out of date and half my breeds are not on there.
Good luck, whatever you decide. Keep us posted!