Hi XXXXXXXXXX

Let's start with building materials. Any framing should be done with pressure treated lumber. Styrofoam (blue or pink closed cell, not white) insulation should be used to isolate the room from any potentially cold walls. If you are in a cold climate a minimum of 2" foam should be used on outside walls. The foam can either be installed behind the studs or between the studs. The partition finish must be water & mold resistant. GP makes a mold inhibiting sheetrock called "High performance". If you plan on tiling the walls cement backer board is suitable. Any of the wall surfaces should be water proof so if you don't tile you could use 1/8" x 4' x 8' pebble texture fiberglass panels. The ceiling should also be waterproof and can be covered with the above mentioned materials. Air quality and humidity are best controled with an air to air heat exchanger with a stainless steel heat exchanger. An air to air exchanger exhausts interior air and uses the heat from the exhausted interior air to warm the incoming fresh air. This unit may be sufficient to control humidity in such a small space. You need 1 air change per hour. The smallest exchangers should be adequate but you should check the specs on units that are available in your area.

The paper on regular sheet rock will harbor mold and in this environment mold is the enemy. If you cut away the bottom several inches from the existing wallboard preventing water from wicking up from the floor in the event of a water spill you could leave it in place but the best practice would be to get rid of it.
You don't need a vapor/moisture barrier since your wall/ceiling surface will be water proof it will act as a vapor barrier. If your wall finish is not waterproof and continuous (no gaps in the water proof area) then a vapor barrier would be advisable. The high performance rock is a gypsum product but it has a treated fiberglass surface instead of paper. There are probably other manufacturers of a similar product. There are some mold inhibiting sheet rock products that have a paper face. I would avoid these.