Not knowing exactly what kind of door yu have, it's usually best to paint it in place on its hinges. You must manhandle the door to rehang it, and the paint will usually get thumbprints from it. I remove the weatherstripping so even when the door is closed, it's not in contact with the frame at all. You can secure it in place with a shim on the edge to ensure that it cannot rattle back and forth. My meaning is that you can close the door as soon as you finish the last stroke of the brush.
I prefer to use oil paint, and found a brand of polyurethane enamel that will set up to touch in about 6 hours. The weatherstrips can go back in the following day.
If there is other work going on at the property, it's best to make sure no dust-generating activities are carried out nearby, and barricade it well; caution tape, x-ed boards, sawhorses, open threats of violence; whatever it takes. Tie up the dog, and lock the cat in a safe room, etc..
Casey

great idea! Thanks so much! It's a metal door. What brand is that oil paint that you have used?

If taking the door off the hinges is a better way to paint, there are things you can do to secure the open area. You could get a piece of cheap fiberboard and place it against the inside frame with a chest of drawers behind it. Or you could cover the open area with heavy plastic and ask the police to do drive-bys of your house.

Be careful. The factory primer is just to make it look better while it's sitting in the rack. it can do more harm than good if it's too old, therefore to do the best I would re-prime.
If i was doing it myself it would be a first quality acrylic finish coat. i would only use oils if I was letting my body man do the job. Acrylic will dry in 45 minutes but will need 2 weeks to CURE, so be careful in that amount of time if you're going to close it tightly, less of a concern if you re-prime.

Re prime and do NOT use oil for the exterior, that is just wrong.