All you need to ship the car through the military is your orders, registration, title, and your passport. If you don't have a title you need a letter from the lien holder stating that you are allowed to take your car overseas. It also has to be cleaned thoroughly inside and out, with nothing in any of the compartments.
Picking up the car seemed to be more of a hassle. The website for our military installation does not give good instructions on what to bring with you to get the car registered or pick it up. You need proof of insurance (unless you have USAA which can be looked up), drivers license, stateside registration, and all the paperwork that they give to you when you drop it off. Looking back I don't know why I didn't just bring absolutely everything with me the first time, but you live and you learn.
I am so excited to finally have our car. I wish we had been able to ship it earlier so that we would have had it earlier. I'll definitely try to do that next time.