Plain old smooth finish is never out of style, IMO. Just remove the popcorn
and paint.

Beware that older homes can have traces of asbestos in the popcorn
ceiling. I suggest getting it tested (most professionals will include
this in the estimate, and might even be required by law). If you will
be doing this yourself, make sure to wear a mask. It's probably a
good idea to seal off the room with plastic sheets as you're in for a
lovely mess.