What's the correct classifier for `房子`?
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.