If it has not been painted before you should prime it with an oil based primer such as Zinsser Cover Stain and then finish with a flat latex ceiling paint. This will stop any bleed thru from the drywall if they did not prime it before the popcorn was applied (they usually don't) and lock it down so not as much will fall down when it is painted. The best way to paint this type of ceiling is to spray it but that is not always
practical, so if you roll it use a 1 to 1 1/4 inch nap roller.

If you use a roller, make sure the paint or primer is very thin. If it is thick and sticky, it will pull the texture right off the ceiling as you roll.
Go gently and carefully.

Also available is a foam roller that has several slits cut in it. It is designed for popcorn ceilings and works well.
good luck

Moreso than the paint, I would strongly recommend using a sprayer. You not only get it done much quicker, but the coverage of uneven surfaces is much better with a sprayer.

The problem with using water-based paints is that it will soften the compound used to create the popcorn finish and make it easier to come off. It also could absorb through the material and fall off due to gravity. However, if you never touch it (e.g. by using a sprayer and not a roller), then it will harmlessly dry with the paint. Moreover, spraying it will prevent "rubbing" the paint into the popcorn. With a sprayer, it will likely stay on the surface and not absord deeply into the popcorn. Indeed, the paint "dries" just a bit while being sprayed through the air, which reduces drying time.