You’ll want to make doorways and stairwells the last thing you paint. Why? Well, this allows you the occasional (and hopefully rare) slam into the wall on the way up the stairs with furniture, or a bounce off the doorjamb on the way into the room. You shouldn’t have to run the risk of needing to go back and re-paint what you’ve already done. Spare yourself the effort and do those first and final coats after the rooms have already been arranged.
One of the benefits to painting before you move your furniture in is that you have all that open space to use effectively without any concerns of dripping paint on your valuables. At the same time, you don’t want to risk chipping or dinging up that fresh coat of paint when the time comes to move all your furniture in.
Not only will the paint look fresh, but you’ll save yourself any extra work along the way. And trust me, after you’re all moved in, the last thing you want to do is create more work for yourself.