I'm building a 3-shelf hanging wall unit w/ beadboard backing for my bathroom. Similar to this stock photo:
It will be painted - rollers and foam brushes. I do not have the equipment to spray unless it's from a rattle can. Assembly is home store Pine, dadoes, Gorilla wood glue, and brad nails.
I'm worried about humidity and wood movement. The room is small and steams up very easily. Obviously, all "exterior" parts will be painted, but should I paint the back of the bead board also? Should I paint the back of the shelves before applying the bead board? Is there any particular type of paint that will seal it best w/ a semi-gloss finish?
Bathroom = high humidity...so, yes, definitely paint ALL surfaces of the wood.
Any good paint (I'd use oil-based) will work, but what I'd really recommend is one of the pigmented finishes intended for marine use. If you're located somewhere near the sea, there might be a chandlery nearby that carries marine finishes. They're usually pretty pricey, but you're only gonna need less than a quart, so it shouldn't be all that bad. Jamestown Distributors carries a good selection if you can't get it locally.
All surfaces it will be, then. I'll use a nice oil-based... While the urethane based product you linked does seem fantastic (and I'll be looking for uses for something like it), I can get a quart of oil from Lowes for $12.