You're not gonna like MY answer anyway...;-)

Until you get a good exhaust-fan (some with light(s) if desired) set up, no matter what you do in there WILL start to suffer...sooner rather than later.
You'd literally be wasting all your time/$$/effort if no fan is installed.

It's THAT important.

Open windows can make things WORSE. If it's a cold day and the windows' open, condensation will fog the air & surfaces even MORE.
Plus...the window-sills themselves will rot sooner.

You're only hurting your home, and in the end COSTING yourself money, by not investing in projects like this.

Faron

Not to contradict what Faron said but I had no fan in my bath for 25 years with no problems( and I had wall paper in there),just let the doors open a little duing showers. The fan is still the best answer, but to answer your question. Wash the walls and ceiling with a bleach solution( 5 to 1, I think)sand any rough areas where paint is peeling, skim with joint compound if needed,sand again, clean all dust and paint with this.

Ps, I hang wallaper for a living, so made sure it was not going to fall down.

Here is a link that might be useful: bathroom paint

Thank you both for your replies. Faron79, with two kids in college right now and one more in another year, there's no money for a properly installed fan; since the roof has to have a hole cut out, it's important that it be done right. Christophern, What is joint compound and what is it used for? Yeah, I sure don't know much about the painting process! I guess the Zinsser sounds like the best bet if I can get it tinted somewhat; don't want all-white. Thanks again, guys (I assume,) for the advice.
Erin

Not to be harsh but if you do not know what joint compound is, you probably should not be taking on this project. Still sound harsh but it is not ment to be.

Here is a link that might be useful: joint compound

No offense taken. I have to learn somehow, don't I? I can't see why I would need joint compound as the cracking is only just under the ceiling on the walls. Really, this is just a simple bathroom paint job and I'm certainly not selling the house, or anything. Thanks again for your help.

P.S. I really hate to write this, but I'm a s-a-h mom, not a tough guy who should know these things. That was rather sexist of me to say, wasn't it? Now, my sisters would know just what to do, but they live elsewhere.

Joint compound is really just a generic term that could mean any kind of spackle, mud, patching compound, etc. It doesn't mean that is only for filling joints. The most user friendly stuff out there is Plus 3 by Sheetrock. It's very lightweight and sands easy which is important for a DIY'er because the biggest mistake they make with patching is putting too much on.....and then they have to sand forever. Several light coats is better and less dusty than one big heavy one. I always tell people to stay away from that Red Devil crap they sell at Ace because you almost need a belt sander to sand it smooth.

Hi again Sjerin,

I aplogize if I came across a little too arrogant or "know-it-all"...which I surely DON'T, LOL!
Sometimes I'm a little "Too realistic"!

Christophern has a good point...
Between leaving a door or window open, choose the door!
(I realize for Women that may be a different issue...)

Separately,
Depending on your Baths' layout and location relative to exterior, normally...fans are routed to a sidewall, with a louvered cover of some type on the exterior.
If you know a good "Handyman" or Trades-person, you may get it done for $200-$400?!?
(most of that is labor)

Faron

Oh, no, faron79! I didn't take anything as arrogance, believe me. I was hoping to hear from the paint pros, of which you are one. I truly do know that it would be the best idea to get a fan installed, but we just can't do it now. Everything costs more in CA so I'm thinking that estimate could easily be doubled, and maybe more.
Paintguy--I'll look for Plus 3-- I'm glad to know about that. I just noticed today that other than a small area in the bath/shower tub, the mildew and slight cracking is in the ceiling paint, which we didn't apply; (we've been in this house 13 years.) I'm thinking that because of that I'll use the Zinsser on the ceiling but maybe BM on the walls, since the color choices for Z are terribly limited. I have to kick my dd out of her bathroom for the weekend and really get in there with the sander and get the prep done. Wish me luck!

Depending on where you go, you can probably have the Zinnser paint tinted to match a BM color of your choice. I'm not positive though..sometimes there are limitations to how much tint you can add to certain products and I don't use that paint so I can't be sure. But, it may be worth it to ask. The BM paint would also be fine though. There are small packets of mildewcide you can buy and add to any paint also. You can even have the guys at the paint store add it in and shake it up for you. That's all Zinnser's bathroom paint really is anyway....just normal shiny paint with mildewcide added.

Hmm, is there a reason you don't use Zinsser? It just seems so easy.... Are the add-in's as good as what is in Z.? Will the paint store add it in for me? Thanks.

No, there isn't really a reason I don't use Zinnser. There is certainly nothing wrong with it. I'm just saying it is simply a high quality paint with mildewcide added and I can add that myself or have the paint store add it for me into whatever product I choose. If you are choosing a BM color, it is just easier to choose a BM product and have them add the mildewcide manually IMO. Will your paint store do that? I know that mine does...I assume all do, but maybe not.

Yee-ha! I'm pretty much done, apart from a window sill, door frame and cabinet doors which shouldn't take too long. What a big job; now let's hope we keep that mildew at bay. Thanks for all the great advice.
Erin

Where can you buy the mildewcide packet? Lowes & Home Depot?

I buy them at the paint store. I'm not sure if the big boxes carry them.