[Nyororin]

Let`s not forget 自宅 and 家庭, which are also "home" - just with different nuances.

The big reason I posted though is this -

家(うち) isn`t really just to refer to your own home - it`s used pretty normally to refer to other people`s homes too... And is pretty frequently shortened to んち from "のうち" in those cases.
For a child, お家 (おうち) is also the standard way of saying house.