I want to create a Shower water controller using an Arduino and 2 stepper motors for the hot and cold water. I have no idea where to start, which Arduino and what accessories?
I thought about removing the faucet handles and modifying some to attach two the stepper motors with gear reduction if needed.
It might be easier to use large servos with faucet valves as they are usually easy to turn, and full rotation is usually less than 180 deg. (at least mine are).
Servos do sound like an easier approach to get working, but I'd have thought that any existing valves/controls would be inside the shower cubicle and that's a pretty hostile place for any electrics/electronics.
Perhaps you could approach this by using the Arduino to control valves in series with the existing mixer valve / taps rather than control the valve/taps directly? I assume that you will be concerned about the possibility of scalding in which case a sensible approach IMO would be to design your system to restrict the hot water flow to keep the output temperature below the target. This also has nice safer failure modes - you always have an unrestricted cold water supply and always have the option of shutting off the hot water using the existing manual controls if something goes wrong.
I have no idea where to start
First start with a monitor of the water temperature and the water flow.
use leds as indicators when some (configurable by potmeter) threshold is reached.
Read about PID control in general, then read about PID with the arduino