I can't remember offhand what your visa status will be when you immigrate but, if you have PR or a long term WP, then education will be at domestic rates rather than international, which can be quite expensive. By domestic rate I mean that you only contribute a small sum now and then I believe, but someone who knows more about how this works can hopefully fill you in.
Medical expenses too would be cheaper than if you didn't have residency or a WP. These expenses will be the same when you are newly in NZ as when you've been there a long time. When you ask about subsidies and benefits, do you mean like Child Benefit? There is something I think is called Family Assistance that you get if you have kids. Previously I think you had to be in NZ for 2 years to qualify for this but it may have change so that you either get it almost immediately or not long after you've been in NZ. Someone will correct me if I've got this wrong.
Just how far $2000 would go depends really on how well you budget. Some people find it easy but others struggle. As Alan says, his family manages on that amount, so I guess he's got it sorted.
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Mother Bear 
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