Regarding the nails vs. screws, I still don't get it and I probably never will. Pros must know something I don't because I see a lot of drywall hung this way. (Then again, I see a lot of building mistakes propagated for no other reason than "that's how I've seen it done.") IMO it's easier to screw in a screw than hammer in a nail. You can preinsert screws just like you do a nail (and I often do). Screws leave no big hammer marks to be filled in, and you have no hammer blows to weaken the drywall. If you make a mistake and have to take out a piece for some reason, screws are easier and less damaging to get out. It's all screws for me.
Anyway, ceilings are supposed to be installed first, for the basic reason that the wall drywall will help support it. But I think this is overstated. Most of the ceiling has no support, and we can't allow ceilings to sag anywhere, not just at edges. So a nailing schedule has to be used to fully support ceiling drywall anyway. Also, if you're not pressing the wall drywall firmly up into the ceiling drywall, you're not getting support anyway, and a lot of people don't. Also, that top plate isn't too big so taking up 1/2" of it for the ceiling drywall cuts into your room. Not a big deal, but also as some people mentioned if working alone you can use the wall drywall to support the ceiling drywall while installing (you have to get the wall drywall hung at just the right spot for this, which isn't easy either.)
Bottom line, one of them has to go first, so it might as well be the ceiling. But nothing's going to fall apart if you have a reason to do it the other way.