I'm assuming by the tongue and groove that the surface to be painted is horizontal. That's bad news around a bath due to standing water left on the paint. That problem is compounded if it is a walking surface. Neither application calls for a standard latex. The high humidity surroundings (due to warm water vapor rising and condensing on the walls and spilled water) call for something more resistant, such as an epoxy. Sherwin Williams sells a one-part epoxy (ask for Pro Industrial) that I have in my bathroom. It isn't cheap, but it will be there for a long time.
If the surface is for walking, then I'd recommend getting a walking surface epoxy. SW sells a waterborne floor paint, but it won't stand up to humidity. Take a look at Tile-Clad, a two-part epoxy. Once again, not cheap, but it will last.
Now, back to your original question, undercoating. Primer is not going to provide humidity and tread resistance - that is the topcoat's job. Primer is just going to promote adhesion and even color/gloss. SW has Wall & Wood Primer that should do the trick. Of course, check the label for proper primer if you get into epoxies or other non-latex formulas.
Wall Paint - Beauty on a Budget
Wall Paint
If the surface is for walking, then I'd recommend getting a walking surface epoxy. SW sells a waterborne floor paint, but it won't stand up to humidity. Take a look at Tile-Clad, a two-part epoxy. Once again, not cheap, but it will last.
Now, back to your original question, undercoating. Primer is not going to provide humidity and tread resistance - that is the topcoat's job. Primer is just going to promote adhesion and even color/gloss. SW has Wall & Wood Primer that should do the trick. Of course, check the label for proper primer if you get into epoxies or other non-latex formulas.
Wall Paint - Beauty on a Budget
Wall Paint