A second hand Tikka in 7mm 08 or 308 is what I'd suggest. Although, 243, 270, 6.5x55, 3006 would all do you well.
Should be able to find a good price on one with a Burris Fullfield II/2, which would have to be the nicest cheapish scope for typical NZ hunting use.
Some stores have good deals on new Tikka's with the Burris, which would be in your price range.
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