Similar to how you can control the flow of water between a tub faucet and a shower head, I'd like my new shower to control water between a rain-head shower from the ceiling and a handheld shower on the wall.
Can I buy a shower kit that contains a shower head, temperature valve, and tub faucet, and just use it differently somehow? Or is there a better way?
You should be able to get a diverter that will do what you want, often they come with handheld showerheads. Usually they allow you to select one or the other, or both showerheads.
What you want is called a "Diverter Valve". That will give you something to search for, because you will find all different types depending on they style you want and how many shower heads it needs to handle. And example can be seen here: