Yes line the room with plastic after you install the drywall. I'd use greenboard just so I didn't have to paint, but that's a personal choice. The poly is ok after it has dried, but totally unnecessary for this application. The humidifier is way overkill, but again it is a personal choice as is the A/C. How will you heat? Sorry, I didn't notice where you were from before starting this, or if is even an issue.
You can use marble, but remember when damp, it does become slippery. I chose to use Sattlilla tile, which also enables me to use it as part of the humidification system.
Hope this helps.