Doors do not attach to siding and should not be attached through siding. If needed, Siding is cut out at attachment point and a proper wood frame is built attaching to the house. Most common attachment for a storm door or screen door is direct attachment to the preexisting door frame. These stick out in front of the door frame and avoid having to deal with siding since attached to existing surface wood.

Alternative and less formal is to get one of the rolled up screen doors that only need to attach to one side and latch to the other. Still need to cutout siding on attachment side and put molding (similar to what there is around window frames around the sides of the place where the door attaches to the house frame.