I have an Airport Extreme Base Station and an Airport Express in my home that are used to support two stationary computers. And all works as designed.

When I get a new (first) iPhone in September and use my WiFi hot spot, will my iPhone roam between the Express and Base Station as I move about my home or will it just latch on to the stronger signal and stay there? Or what?

It depends on how you configured your WiFi network(s). If you for example use the Express to extend* the Extreme's network, you'll roam and use the best of the two depending on location. If you set up the Extreme and Express as two separate access points, you've got to switch manually between them.

*) the option to extend an existing network is offered by Airport Utility early on in the configuration process.

Many thanks, alternaut. Now, all I must do is wait for the new iPhones to be released.