I would definately vote for spraying. But if you do not, then you will have to roll it out.
Rolling out popcorn is extremely difficult as one, the stuff will fall off and with paint on the particles, it will make a mess on the floor, secondly since it has peaks and valleys, you have to roll it on all four sides. If not, the side opposite the direction of the roll will not have paint and you will see what I mean the next day.
definately use latex paint for sure.
Count on using twice the amount of paint also when rolling and use a heavy knap roller cover like a 1/2 inch or even a 3/4, but watch for splatter if you roll too fast.
If you have or want to spend $60 for a cheap wagner sprayer, and dilute the paint down enough, this will work. I would do it twice as the paint is soo thin. Use a good quality paint NOT from a home center.