Should I use nails or screws for hanging drywall on the ceiling?
There is absolutely no reason to use nails in this day and age. I urge you to use 1 5/8" drywall screws.  There are several reasons.  Screws have much better holding power, they are actually faster to install, and they can be slightly counter sunk during installation to make mudding a lot easier ( especially with a drywall screw gun or a decent drywall bit that can be used in any drill).  Nails can loosen with age and "pop" out through the mud coat, cracking your paint.  The difference in price is negligible, but the difference in performance is massive. Drywall finish is the end result of a room project, the surface you will see for a very long time, don't cheat yourself.  Do it well, use screws and a good gun or bit.  Good Luck.