Hi, Wendy. First, some of the doors that I have seen come with a paint that is almost like a primer on them. I would give them a light sanding just to freshen the surface and rough it up with about 150 grit paper then vacuum and tack rag it. Tape around the window and any other areas that you do not want painted with the main door color with painters tape. Don't use masking tape.
Personally, I would spray with the door laid flat and use spray cans. Either of the kinds of paint mentioned will work just fine and the decision is more to what kind and color of paint you can find at your local auto parts store that fits the bill. Follow the instructions on the can and you might practice on a big sheet of cardboard getting a nice smooth spray pattern. You will probably need at least 2 cans and you will want to be sure that both cans came from the same lot.
After the base color is really dry, you can mask with newspaper and painters tape and do any trim areas the same way. The mist from a spray can will really travel so be sure you mask a large area.
Good luck and let us know how it came out. Henry in MI