I just removed some wallpaper from a shower ceiling. I now have exposed drywall. What type of primer and paint do you suggest I use? I'm overwhelmed by the oil/water/latex bases, and when to use which. It stands to reason, being a shower, that moisture is top concern.
Ideally, if it's standard sheetrock, I'd suggest removing it. You normally want to use 'greenboard' (sheetrock with a waxed paper layer) or, even better, the paperless wallboard products like Densarmor (they use a fiberglass layer rather than paper). The paper is what the mildew will like to 'eat' so removing as much of that as you can, the better.
Barring that, they do make paints specifically for bathrooms. They usually have some sort of anti-mildew additive.
Finally, be sure the bathroom is properly vented. That, alone, is the single best solution. If there is no ceiling fan, invest in that first.
To answer the specifics:
Latex is water based, so that's the same thing. And is what you want to use--specifically ones labeled for bathrooms and high-moisture areas (ie, they have the mildew preventative additive). You COULD use Oil based paint, and that has historically been something to use in a bathroom, but latex paints have come a long way and Oil based interior paint is now a rarity and likely not what most DIYers would want to use anyways (it's a bit more finicky and smelly to apply and a lot more messy to clean up).
You said your removed wallpaper from the ceiling. I'm assuming that the house is old, and the bathroom is old, and the wallpaper has been there a while. (Because who puts wallpaper on ceilings?)
The wallpaper probably trapped moisture against the ceiling, so you may already have the start of a mold/mildew problem.
My advice, for drywall, is to get the ceiling as dry as you can, as fast as you can. If you have a second bath, you might consider opening a window if it's winter where you are (winter air tends to be dry, pulling moisture out quickly). If it's humid where you are, or summer, then get some kind of drying mechanism - a fan, a salamander type heater, etc. Spend a day or two driving as much moisture out of the ceiling as you can.
Once that's done, put on a coat or two of "mold killing primer". Zinser and Kilz both make this and sell it in "big box" stores. I'm sure other manufacturers sell similar products. This will tend to kill anything that is already growing (even if you can't see it), and create an immediate vapor barrier with the drywall.
Pay particular attention to the corners/edges, where the ceiling meets whatever wall you have. I don't know if you have tile all the way up, or more drywall, or what. But the edges are going to be a potential weak spot, so you should really slather it on at the edges before cleaning it off.
Once you have the primer up, you can wait on the actual paint. If you already know your target paint color(s), you might consider asking your paint vendor to tint the primer for you, so you don't have to use so much paint over it.
If you are using the bathroom, you may have to "help" the primer to dry. Don't expose it to cold air, but a heater or a fan or a dehumidifier might be good.