I think I'd be a bit cautious about organising your police checks and medical too early because they only have a limited life. Police certificates last for 6 months and medicals for only 3 months before they have to be done again. You certainly don't need to have them done before you arrive in NZ unless you're pretty sure about getting a job quickly.
Other documents you'd need to take with you would be anything related to your higher education, job and work experience, like qualifications, certificates and evidence of work experience. You'd also need things like your birth certificate, your CV and any job references past and present, photocopies of your passport, driving licence.
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Mother Bear 
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