How do I determine what valve I need when building a shower system?
For maximum safety and comfort it is best to use a thermostatic temperature control valve. A high output thermostatic valve will not only give the needed flow, but more importantly - it will control and maintain the temperature.
The capacity of the valve (GPM output) must be able to handle greater or equal value to the sum of your chosen components. This is why you added the total capacity needed for your components above.
Choose your thermostatic valve based on the amount of water it can handle.