There are at least three ways to divert the water to where you want it. First, and probably most common, is to use a tub spout with a diverter in it. My preference here is the Delta line with a pull-down diverter (not a knob you pull up). They come in many finishes, styles, and either plastic body (lead-free) or brass (who knows for how long, though). Second, some (but not all that many) tub/shower valves have a built-in diverter. Third, a separate diverter valve. These can get pricey if you wanted to control multiple things, like say a rain shower, a handheld, body sprays, or the tub - they can have multiple inputs and outputs...and, it's another hole in the wall and extra plumbing and the trim can be expensive, too. Necessary for some, but not for what you want to do.
Pretty much any single-handle tub/shower valve you can buy works as you indicate. To get extra features, requires another knob or handle. Those with a second control could give you either volume control, or is a thermostatic control. These tend to cost a bit more because they are more complex. Personally, I like a thermostatically controlled valve, and have a Grohe valve in my main bathroom with that feature.