I moved to Auckland three months ago - my family and dog joined me this week. I'd never been to NZ before but have travelled and lived abroad a lot so the emigration thing didn't really bother me.
It cost us about 2k (vet + transport) to get the dog over but that will go up as the law is changing and they want quarantine here for dogs for a short time.
The firm I work for paid $16k relocation which wasn't quite enough for a container, insurance and four one-way tickets but it was close. I think it has cost us around 3k (sterling) of our own money.
I'm loving living here so far. Things are different enough to be interesting but similar enough to be easy to do. Things like getting a car, broadband, phone, bank account etc have ben really easy to do. Renting a house could have been awkward but I got lucky and got the one I wanted first time. I pay $2k/month for a 4 bed house in an area called Bucklands Beach. The house is a 2min walk from the beach. I get the ferry to work, which is great, and then cycle back. Commuting is great as long as you leave a bit after rush hour - the roads in the city are really smooth and a pleasure to ride on.
The place is full of expats which is good and bad. Everything in Auckland is expensive except for meat.
I have found some amazing places 20min out of Auckland but that doesn't even scratch the surface of what is on offer.
There are bars, restaurants, cinemas, a theatre or two, gigs, loads of bike shops etc - not sure what else you could want - although obviously not as much choice as the UK.
Work is ok - I am a civil engineer (although I don't really do civil engineering any more). The way of working is quite different and I'm not totally comfortable with it but I can live with it. I go to Wellington with work regularly and it is a nice city with better scenery but even though I thought I'd prefer it originally I think I will prefer the north during the summer.
Hope this helps. Feel free to email me - onebrucewalton and then it's hotmail uk.