Relatively easy through the Apple Store app
The last time I upgraded, more than two years ago, I had an individual account with AT&T. Now I am on a family plan.
It turns out when they ask for your ZIP Code and the last four digits of your Social Security number, they want that information for the account holder not the person who is upgrading.
It took me a little bit of time to search through my files and find that information.
I wasn't given the option to choose a shipping address. At least I don't think I had that option. It defaulted in to my sisters name and address. Luckily, that's where I wanted it shipped.
The final snag came when I tried to check out. It seemed to hang for a very long time. I decided to check on my computer to see if I could get into the account and finish the check out there. that's when I realized the Wi-Fi network I was on no longer had an Internet connection.
I turned off the Wi-Fi on my iPad, but the Apple Store was still spinning. I guess the app couldn't handle switch to LTE midstream. I killed the app, and then restarted it. The transaction was still there waiting for me to check out, and I did that with no problems.
I have a confirmation email, and a delivery date of September 21. I still can't get to the Internet on my computer over Wi-Fi. Update: it just came back. I don't need it anymore. Oh well.