Cost the of building a house in Alabama would depend on the size of the house, the number of bedrooms, bathrooms, material use, flooring, etc. If you are looking for just a basic home construction then the cost per square foot could be as low as $80 psf.he most expensive room in the house per foot is a bathroom. Add and extra bathroom to a house and while you may add 50 square feet to the house it will cost you nearly $3,300 in plumbing fixtures and labor (that`s an extra $66 per foot over the cost of the bedroom.