For the most professional job, which should I paint first.....my walls or door frames and baseboards? Or ceilings?

We're buying all new pre-hung doors for the interior of our house, and I was thinking how much easier it would be to paint all the trim before we install them. But then they'd probably get all messed up and I'd have to redo them.

We would go ahead and paint the walls before installing the doors, except that we don't have a paint color picked out yet. We're rehabbing a small house, and I'm going to have to buy all new furniture for the smaller space. Until I do that (which will be a bit down the road because there is just too much other stuff to do right now), I won't be able to determine a paint color. Meanwhile, we've just primed the new drywall.

But as a general rule, I've always wondered how the professional painters paint.....what order? And what kind of painter's tape do you use? We've had mixed success with painter's tape......sometimes it has left a residue or even pulled off some of the newly painted surface. Maybe we didn't have a good kind???

Thanks for your help!