It depends on where your job is. Auckland and the cities are more expensive.
We cut it pretty close. Came with only $3500:
- $2000 car (This was what we could afford and didn't want a loan. It took us everywhere but needed to spend on maintenance over time. Eventually got rid of it.)
- $580 rent (1 week + 1 week deposit. Landlady didn't take bond and later regretted it when we spilled food on the carpet but we did pay her money for it.)
- $450 first week accommodation
- Remaining on food until payday.
However much money you decide to bring, do a budget and stick to it.