Using a building wrap and flashing correctly will greatly increase the water tightness of your building. 

Mineral paint contains no VOC's and is another breathable product to ensure no moisture is trapped within your walls.

Using insulations made of natural materials are naturally mold resistant and allow the house to breathe.

Choosing natural products with low or no VOC finishes means you will not have to worry about off gasing exposure in the future.

Lathe and lime plaster or magnesium board are both great options when renovating or building.

There are many other things you can do to improve your space.  Installing a Wi-Fi switch or improve your attic ventilation are both worth while.