I used particle board baseboards in our bathroom a few years ago, but found, even after prepping/painting them, they have swelled up with the moisture in the bathroom (more around the bath area). I was in the store this weekend and see they make a "plastic" baseboard, but see some challenges with cutting around round corners and painting (adhesion). Is there a right material to use for bathrooms?
Real wood. Poplar trim is what I use for bathrooms or basements. It is hard and holds up to moisture well. If you get the plastic stuff it will look like... plastic. It would have to really be in modern room or business setting to look right.
I would suggest getting poplar (pine is cheap and has moisture bulging issues) or some other hard wood. Give it a first coat with drylok. Follow up with whatever you want. I would suggest an oil based paint for bathroom trim though - it is tougher and cleans up better.
For tiled bathroom floors I feel that nothing is better than tile for the floorboards. And if you are using tile on your floor than you can use tile on the base of the walls too. It can be done with the same type as the floor or something different like the glass tiles used as kitchen backsplash. Prep the sheet rock surface properly, seal if needed so moisture from grout doesn't damage the wall. Approximately 2 inches high maximum or you will get too far up away from the wood of the wall's framework and that's when sheet rock will bend when bumped, and grout does not bend without cracking. By the time you seal the grout too, you have finished a big project. Wood might be easier.
Lowes/Homedepot carry a line of trim made of Polystyrene. It's cheap, easy to work with, and holds up to moisture extremely well. It comes in all sorts of styles like wood does and you cut it with your miter saw the same way. It can be nailed with your air nailer or glued in place. It typically comes prefinished white, no painting or staining required. Depending on what you're looking for, it can be a quick easy way to make your bathroom nice. Obviously real wood has it's place too, it depends on what you are looking for. Check them out in person.
I second the recommendation to use "matching tile" (from the floor) as the baseboard. Plus it's water proof and easier to clean.
You probably shouldn't use MDF anyway since it can swell with water.
A few other places recommend 4" high or even 6" (whatever looks good to you, or whatever matches any other "step ups" in your bathroom). Some also recommend not grouting the joint between wall and floor (just caulk there) and also recommend the "grout lines" line up with the floor grout lines, if the floor tiles aren't angled.
It also seems to be up in the air as to whether you want to use bull nose or some finish on the tile used as baseboard. Some recommend using a "profile" to finish the edge, or chrome capping or sloped grout over the cut edge.
Basically your options are to either grout "up" at a 45 degree angle, or you could use a cove or bull nose tile, or possibly add a metal edge trim (ex: Schluter) above it, though that may not work out perfectly since the edge trim sticks out a tiny bit, and isn't made exactly for that (having to be cleaned, etc.)
I've also heard of using marble but don't know much about it.
People told me I was crazy to ask for it, but I am really pleased with cove molded linoleum, which comes up the wall instead of baseboard. The curve makes cleaning very easy and contains spills very well. There's just one thin caulk line at each corner. Like all caulk lines it collects debris:
The true linoleum is 100% natural, refinishable and warm to the feet (though you should consider if underfloor heating is right for your situation).
Epoxy flooring also has huge advantages, with no seams whatsoever, as the epoxy will curve up from the floor to form the baseboard. There's a reason both are commonly used in commercial bathrooms. Why they are rare in residential I can't fully explain.
I would suggest wood baseboards for the bathroom. First, I would paint both sides of the baseboard. When I paint I use a primer; I make the primer the same color as the finish, that way it goes on with one coat instead of painting twice or three times. Second, after your baseboard is in, put caulk on the top of your baseboard and run it all around. If you would like you could do the same with the floor, that way if you have a water spill it does not get behind the walls. You've caught the corners, you've caught the floor, your cocktail per half that's how I would do it.