British Expats - Teachers moving to New Zealand

We are currently researching moving to New Zealand.

I am Swedish, my wife British and we have moved around the world and currently live in Kenya. My wife is Head of Latin at a British school here and I am sudying for an MA in Education and hoping to get work as a secondary school history-teacher, I have a BA in History. I emailed the NZ Association of History Teachers and they seemed positive and told me to contact the NZ Teachers Council which I have but no reply yet. Neither of us are currently registered teachers as such but if necessary, we could take the relevant courses.

I just wonder about the possibility of getting into New Zealand and the ways of doing it. Am I correct in thinking that we could either submit an EOI and then hope for a PR or we could apply for a job and with a job-offer apply for a work permit?

I assume that the New Zealand economy has suffered like everywhere. Is getting into New Zealand hard these days or are they still looking for people? We are a, relatively, young family. I am 36 and my wife 37 and we have five kids aged 12-3. We both have, or will have, Masters and at least two years relevant work experience. Do they take the fact that we have kids into account? Is that an added benefit or not?