Bleach will not kill mold. It can actually feed it. In simplistic terms, think of bleach as being "bleach" and "water". The "bleach" part, because of it's chemical make-up, will not penetrate into many materials. It doesn't soak in. It simply sits on the surface. The "water" that carries the bleach? It does sink in and penetrate many materials. And what helps create an environment for mold and mildew to thrive? Moisture! When people use bleach, sure the discoloration of the mold goes away because the mold that sits on the surface is indeed killed by the bleach, and the discoloration is "bleached" away. But the water penetrates, feeds the roots of the mold, and the mold will usually return. Try this product to actually kill the mold: Concrobium Mold Control. It's available at the box stores. Kill the mold, then prime with a primer/sealer from the Kilz line. Or with any other good primer/sealer that you can find. Then paint with any decent bathroom paint. The Concrobium will kill the mold and mildew. The Kilz primer/sealer will prevent any stains from the mold/mildew from being activated by the primer or paint and bleeding eventually bleeding through the final coat of paint. You can do more than one coat if you choose. Just read the directions for recoat times. My recommendations at least. Just an opinion.

I really don't think there is such a thing as a mildew resistant primer and this makes sense to me as being something that is not needed because mildew will not grow on primer. The primer is under the paint that you use as a topcoat so when will primer ever be exposed to moisture? In order for mildew to grow, moisture is required. I think the recipe for getting your paint to hold up nice in a high moisture environment is using high quality products like a top line primer and a top line paint. You can add a packet of mildewcide to whatever paint you choose to use as a topcoat which should make it resistant to mildew or you can buy Zinnsers Bathroom Paint which already has that added. I'm sure other paints have mildewcide in it already too. I like hot showers too and I have a shower in a very old house with a painted ceiling in it. It's holding up great for 7 years now and I never even used mildewcide. I guess if you can have a bathroom where moisture doesn't sit around for long periods (it dries completely after each shower) then you will be good.

Bathroom is 11ft long by 7ft wide.

For a more modern log home you would pick colors the same way you would in a regular home - bring all your pieces together and draw a color out of them...if you are really feeling the country then you may want to be in sage greens, pumpkin, fall reds and things like that. I do agree - no need to paint before cabinets go in - don't rush... find colors you are drawn to and paint poster boards and hang them up and look at them for a week or so... Good luck!