Somebody built that house because it was their dream project, and then sold it because it turned into a nightmare.

If you want a thick stone house, you will need to acquire and move the stone. The usual construction in the US is wood stick framing. It's so ubiquitous that even finding a contractor who will work with steel framing instead of wood is difficult. The material cost isn't awfully different, but the techniques are.

Finding a contractor to handle stone would require a much, much larger budget.