What's the correct classifier for `房子`? In my little bit of Mandarin experience, I have got that the classifier for 房子 is 座, and also felt that 座 is usually used to refer to a building. However, I have just read that someone here over Chinese Language Stack Exchange says the classifier is 栋, and so I wonder which should be used to refer to 房子.

Later I found that the classifier for 房子 may include more; in this online dictionary, it shows 栋, 座, 套, and 幢. So I wonder how I can decide which to use and also like to know why.

Also, even if the proper classifier for 房子 is 栋, could I still use 座 in that context? Or do they give two totally different meanings?
All of them are OK to use to classify 房子, it depends on the type of house itself, which one is considered the more adequate. 


幢 is preferred when speaking of large and tall buildings
栋 tends to be used to refer to buildings that are wide
座 is used for buildings that are “stable and steady", e.g. palace, temple, large mansions (mostly with public purpose)


Source: Chinese University of Hong Kong 

As for 套 I have no reference, I suppose it has its own specific set of buildings it can classify.