No reason to paint the inside

thanks, but where do you stop? Do you paint the sides the same as the outside?

The edge you see standing outside looking in, is painted the outside color. the edge closest to you opening the door is the interior

Paint it any way you choose. If the door is close to the frame, I'd advise against painting it (the edge I mean). Particularly latex, even 100% acrylic. It tends to 'block' or stick, especially in hot or humid conditions. Prime with an adhesion promoting primer, then with 2 coats of finish. If you are handy, it's sometimes easier to remove the door from the frame, lay flat and paint that way. Less runs if you are heavy on the finish. You can tape up plastic while the door is down to stop airflow while you work.

Thanks for the warning about painting the edges.
And, the paint to use. I appreciate the info.

Painting the edge is very, very important. Most wood doors lose warranty coverage if edges are not sealed or painted. Edges are more vulnerable to moisture infiltration causing expansion and sticking, warping, etc.. Unless the door is rubbing on the jamb, there is no reason not to sand the edge smooth and repaint it. Most doors have at least a 1/4" gap between door edge and jamb which is filled by the weatherstrip when closed.

just remove the weatherstrip before painting for a couple days and there will be no blocking as posted above