Stepper motors are not a good choice for this application as they will use more power than the solar panel produces.
Use a cheap DC motor with a worm gear drive. Then the motor only needs power occasionally when the panel needs to move and the worm gear drive will not allow the panel to move when the motor is off. If your panel is heavy a used car windscreen wiper motor might be a good choice.
Programming the movements based on two LDRs should be very straightforward. Just arrange a shield so that both LDRs only get full sunlight when the panel is pointing directly at the sun. Then your code will move the panel in the direction of the LDR that is in the shade.
I suggest you make a proper cover for the mechanism rather than bother with the complication and power wastage of moving the solar panel to protect it. In any case, if the project is outdoors it needs to be protected from dust and insects as well as rain.
...R