Do we simply apply for a work visa and at the same time submit EOI as we then have the job offer giving us enough points?
Yes. You would also apply for partner-sponsored temporary work visa for the spouse without the job offer, and student or visitor's visas for children (depending on if they are of school age or below), to match the work visa for length of time. This would mean the whole family could be working/schooling in NZ while the residence visa for them all was taking the necessary time of processing. Another advantage to applying for it all at once is that a lot of the evidence would be shared.