If you click on the initial letter of your country on
here it should take you to instructions on how to make your application for a police certificate.
You can apply for your own Work Permit but you will need a job offer and confirmation of this to show to INZ before you do it.
You can look for somewhere to stay on such websites as
AA Travel
Accommodation NZ
Asia Rooms
Aspen House, Auckland
Motel accommodation
City Life, Auckland
Jason's (site was down when I checked the link)
Moana Vista, Auckland
Perhaps some folks on here might have some personal recommendations.