Hi, I would say based upon where you live. What time your girls go in for the night, what time is sunset and sunrise. It will change throughout the year and you'll have to re-adjust. Just watch them, if they are all in by, say...7 pm and it's almost dark, set your timer for door closer for that time. I had to adjust mine several times so my door is not open too long once they are all in roosting. Good luck.
Light timer. I prefer to have the birds awakened at the same time, year around. 5 am. I allow the light to snap off at 5 pm, year around as well. Thus, they naturally get a much longer day during the summer than in the winter. I don't push them during cold weather, as I want them to use their energy for staying warm. Egg production drops by 20% but that is quite tolerable.
By having the light turn off at 5 pm, they always go to the roost with the setting sun. If I waited until 7 pm to have light go out, it would plunge them into total darkness, instantly, during much of the year.
Cannot help you on the door, but I don't let the hens out before noon. Most of the hens lay before noon, so they have work to do before going out to play.