They will need to provide strong white illumination of about 300-400 lumens.
That sounds like a power LED is needed, these require special circuitry to drive them. This is called a constant current supply. You can buy these but the cost will add up.
Two curtains of approx 500g will need to be drawn and closed by their own motors (they will be closed by gravity).
You will need something like a micro switch to detect when they are open so you know when to turn off the motor.
10 green, 10 red and 10 amber LEDs will be required to flash on and off.
Looks like you will need at least two port expanders of the 23016 type.
but I could really use some help with picking the right electronic parts
It's not just that it is putting them together, for a first project the is way over ambitious.