Flat absorbs moisture, so don't use that. Use something with a gloss,
which provides a hard-shell barrier. How much gloss -- semi-gloss,
gloss, high gloss -- is up to you. Satin would work too.
I'd do 2 finish coats and avoid using the shower the day you finish the
Latex works fine -- if you want to use oil-based, you can, but I find
it's unnecessary. And you have to keep using oil-based if and when you
decide to repaint.
"Ceiling paints" are typically flat and denote nothing more than a
particular color. There are probably ceiling paints marketed for
specific applications, but it's nothing more than marketing. It's like
that hardware store that use to advertise "Kids Paint" -- a special
paint for kids' rooms that allowed you to clean the walls. All it was
was regular satin finish latex paint.