Don't plan on any of this happening quickly - although if they know you have a job offer and the job is being held for you they might hurry things up a bit but they have to check that the job meets the criteria and that all the boxes have been ticked i.e. no resident kiwi can do the job, the job has been advertised for at least 3 months prior etc, etc.
You can get your work visa if you have a job offer and it's all been approved as above. Your family can accompany you on a work visa, your wife will be given a work visa as well if your application is successful but your kids can't study without a study permit and you have to have a work visa before you can apply for one of those unless your kids are being classed as international students which means they have to pay international fees.
We came out on VV's and applied for WV's once we were offered work. We were offered jobs within a few weeks, it still took 2 months for the WV's to come through and another 6 weeks for the study permits. We arrived in July and our kids didn't go to school until December. It didn't do any harm and they settled in really well but it was quite difficult keeping them occupied all that time without any friends around.
Good luck
