Metal door/ wood screws
If necessary any screw will secure the brackets to the door (in most cases). The reason to use sheet metal fasteners is to penetrate the metal door skin. Once the tip of  the screw is past the metal surface it grabs and drills into the wooden frame work. The wooden skeleton of the door is the 4 outside edges and the 4 sides of the window. Your best bet for successfully attaching to the wood frame is to remember the frame extends about an inch wider than the windows perimeter. Keep your brackets (if possible) under an inch past the windows edge. It's the wood framing that is supporting the brackets. So if you drill an opening in the metal skin any screw will suffice.