I would think, for speed, you could apply for a Work Permit to get you started in your job and then submit a PR application to run alongside it. If you get a WP, your wife and children should be able to get appropriate visas i.e. WP and student visas under the same application. Otherwise they could get visit visas for 6 months (if you're from the UK) and extend up to 12 months if you're still waiting for the PR to come through. The problem with the latter is that you'd have to pay international fees for the kids' schooling until PR is finalised.
E4.5 Spouses or de facto partners and dependent children of student or work visa or permit holders
Spouses or de facto partners of student or work visa or permit holders may be issued with temporary visas or granted temporary permits of a type appropriate to their needs for the currency of the spouse or partner's visa or permit.
To be eligible for a temporary visa or permit, spouses or de facto partners must be in a genuine and stable relationship*. For de facto partners the couple must also have been living together in a genuine and stable relationship* for at least 2 years immediately before the application is assessed.
Dependent children* of student or work visa or permit holders may be issued with temporary visas or granted temporary permits of a type appropriate to their needs for the duration of the parent's visa or permit.
Spouses of full fee scholarship students, who receive a 'dependant's allowance' from MFAT, require MFAT's approval to be granted a work permit.
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Mother Bear 
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