They might put you in contact with another graduate student, possibly in a similar situation, that could help you know where to look for houses/apartments. The schools themselves might also have resources, such as apartment lists, room share requests, etc. It really depends on the school and area though. I attend a university where a great part of the student population lives off campus, so the resources are immense for both graduate and undergraduate students.
If you are offered a package that includes health insurance, the school will set that up for you. You will need to sign a few documents at the beginning of the year, but you will probably do that with the rest of your employment papers. I would probably make sure you ask human resources about the health insurance details before you accept an offer so that you know who and what the insurance will cover (for example, our student insurance is very cheap, but once you had a spouse it skyrockets, and since I don't have any dependents I don't know whether it would adequately cover a family or not).
Good luck!