We get questions on how to build out a basement and not worry about mold. Here is a quick 5 step process to a mold free basement build out.
#1. Put a concrete sealer on the floor and walls. Anything concrete sealer will do. If you are worried about seepage then you can use ULG DryLok http://www.drylok.com/ This will stop the moisture from the ground evaporating into the house. (Less of a musty smell)
#2. Use a product called InSoFast to insulate and frame all the exterior walls. This will frame and insulate in one step. We have used this numerous times with great results. (and it goes up fast) You do have to run your electrical before you install the wall panels. Once the exterior walls are done you can frame up the interior walls with steel studs.
#3. Install Dens Armor Plus drywall http://www.buildgp.com/densarmorplus-abuse-resistant-gypsum-panels This is a fiberglass faced drywall (No paper) so it will not get moldy.
#4. If you are going to paint all your trim, then you can use Azek trim for baseboard and casings. https://azek.com/products/moulding This is a PVC product and also will not get moldy if you do take on water...
#5. Your flooring can be ceramic tile, a vinyl flooring or an epoxy coating. They come in an unlimited array of colors and styles. it will be easy to find something that works. If you want carpet, use an area rug. that way if you do take on some water you can take it out and have it cleaned or replace it.
This will create a place very difficult for mold to grow. (no food, wood fibers)
If you have a flooding problem, then you may want to install drain tile around the perimeter of the basement and install a sump pump.