To spray doors correctly takes a little time and effort. Each paint contractor has their own idea about how to go about this and there are various “systems” available out there that will supposedly make the job easier. Many Painters in Omaha will pick a room and tilt the doors against the wall and spray them that way and then flip them over to spray the other side. There isn’t anything wrong with doing it this way if you can control the overspray and deal with the wall that will have many door shadows on them after spraying. This method is very common in new construction.
The way we prefer to do it is to do any prep work while the doors are laying on saw horses, sanding,etc., and then “soldier stand” the doors. That’s the term I use, I don’t know if anybody else calls it that. When you soldier stand doors you stand them upright and form a zig zag pattern by attaching a piece of wood at the top of the door. There are metal brackets sold for this purpose and I have recently seen a plastic bracket that you attach the doors with that connects at the door hinge screw holes. I am not a fan of plastic anything so I would pass on that.
The beauty of this system is you can spray all sides of the doors at once and you get fit a lot of doors in a smaller area. There is no overspray on the walls you would have to sand and prime and overspray is manageable. We normally use wooden shims and put two nails or screws per door. The zig zag pattern helps provide stability to the doors.