Hi wimwom
General advice is to bring EVERYTHING with you, it will cost more to replace than to ship. That includes furniture, clothes, everything you can think of.
Maternity care is free if you're a resident, citizen or on work visa of two years or more. Details here
www.health.govt.nz/your-health/services-and-support/health-care-services/maternity-services
You choose an LMC (Lead Maternity Carer) who does all antenatal care, is there for labour and birth and does a few weeks of post-natal visits too. It was actually really lovely having the same person from that first phone call at a few weeks pg till having a 4 week old baby - I was quite sad when I said goodbye to my mw.
Problem for you is that if you're not arriving here till 20wks pg you may find a lot of the mws don't have any spaces left, they get booked up early especially in busier areas. I think you can go under the care of a team of hospital mws if this happens - not quite the same continuity of care as with one mw.
I've had two dcs on the public system and thought the care I got was excellent.
You can go private if you want to, I know a few people who have, think a privAte obstetrician costs about $5K?
Where you choose to live may be affected by where jobs are due to commuting times etc. Furnished rentals are quite hard to find I think...search on Trade Me rental pages and put "furnished "in the search box maybe?
www.trademe.co.nz/property?cid=4233