https://www.immigration.govt.nz/new-...ills-work-visa This job is on the Immediate Skill Shortage List for all areas,
http://skillshortages.immigration.go...chanic-general, so your employer does not need to go through the labour market check.
This
https://www.immigration.govt.nz/new-...k-visa-holders is the visa for your wife, and there is a link there to the page for the visas for your children. You can apply for the whole family's visas at the same time, linking them with a covering letter, and INZ will work it as one case, and will supply your visa number, etc., which you won't know at first, as it becomes available.
With this job, you will also be able to apply for Residence for the whole family under the Skilled Migrant Scheme.