nice gaijin, you took the words right out of my mouth!
Rent should already be assessed (maybe even paid for!).
Living expenses: They should have given you SOME idea by now!
Schools: Ditto.
Figure on needing about 300,000 yen/month just to live on, schooling not included, if you have to pay rent. Depending on where they set you up (with a family it'd better not be in some dormitory, but it might be in a low-rent or older apartment complex that other employees share), you might be close to work or not.
Whatever the case, you and your wife had better start learning Japanese now. She's going to be exposed to just as much, maybe more, in daily life.