Everything needs motors and internet connectivity.
The project needs to be done in steps with no particular order.
A. Measure torque to open and close several types of blinds. Off to SEARS!
B. Select a motor that can meet that torque value and will not be loud.
C. Select a battery that can deliver enough power to the motor to run, run the wireless module, and run the arduino.
D. Select a solar panel that can fill the battery even on overcast days.
E. Design a charging circuit to marry the battery and solar panel.
F. Design control circuit including the arduino, wifi module, and motor driver.
G. Solder the board.
H. Assemble circuit and test.
I. Print housing, assemble, and test.
J. Ongoing improvements to design.