Maple is a great wood. Personally, I would stain and finish if the door lends itself to this type of finish. But, paint will do nicely.
Here's the steps to take to paint your maple door;
1) Hand sand all wood surface. A smooth surface is important. Take note of any deep gouges, scratches or cracks. They will be fixed later.
2) Apply two thin coats of a oil based wood primer. Allow to dry completely.
3) Repair any major defects. These are the cracks, gouges and dents you found when sanding. Use a good wood filler to repair any defects.
4) Lightly sand once more. This will remove any heavy brush marks or any dust that settled into the primer after application. After the dust is removed you are ready for painting.
A high quality 100% acrylic exterior paint should be used on the exterior side. The interior side can be the same trim or door paint used through out your house.