The statement Mongo makes here about High Quality Primers is great!
I have always used Benjamin Moore paints for most purposes, but I have discovered Brunning's "Grabber Plus" Primer. This stuff is incredible for this type of area. Keep in mind that this stuff is an adhesion primer and it will stick to anything that it is allowed to dry to and you will have a bugger of a time getting it off. For a finish, I'd recomend using Zinnser's "PermaWhite" ( can be tinted) or Ben Moore's Kitchen and Bath Paint. Both will not support Mildew, making the use of a mildewicide unnessisary.