I agree with Namisuke.
Get the basics of schools, logistics, expected bills, maybe basic info on the JTEs (ie, names and how frequently you will work with them, and maybe whether or not they are open to games or stick pretty strictly to the book), and clothing stuff, however there is such a thing as too much information.
My pred gave me waaaaaay too many details about each student, the students brothers and sisters, the cousin relationships, the relationships between teachers, the relationships between the students and the bankers... etc. It's a small town -- I could have found that stuff out for myself, and it would have meant more to me that way.
Only things that I really wish I had asked other than my initial questions (which were basically those I listed above) was about what places in town are open for dinner in the evenings.... but even then, finding that out on my own has been pretty fun... and I've found a few hole-in-the-wall treasures for dinner when I don't feel like cooking for myself that I don't think even my pred knew about.