ATT web site did not offer me the older plans (like 3GB/mo) that I have to select for my son's phone to keep my unlimited data plan. The web site offered only Family Share plans.
I bailed.
The Apple site, however, gave me all the choices. I upgraded using Apple's site. (see below).
I will visit the store to set up my upgrade as I want to trade in my iPhone 5 (for $200). That can be dome only at the stores, apparently.