How can I apply for a work visa to research investment opportunities for an investor visa in New Zealand?

If you have been approved in principle, you can apply, as the principal applicant for a one-year work visa to arrange for the transfer of funds. The family can apply for visitor visas for the same duration. In terms of the detail I suggest you either visit the immigration website or engage the services of an immigration adviser.

You could either apply for a visitor visa or an investor visa and upon AIP, you can apply for a work visa for that purpose. The difference is you won't be able to work with a visitor visa for obvious reasons.

After you have received the approval in principle (AIP), which is the direction from Immigration NZ that they are satisfied the requirements to date are met, you will be advised that you have 12 months to transfer the funds and make the acceptable investments in New Zealand. It is policy to allow you to apply for a work visa with multiple-entry travel conditions for 12 months after the AIP. Your partner may apply for a visitor or work visa,  and your children may apply for a visitor or student visa. If you want to travel to New Zealand before the AIP decision, you will need to arrange a visitor visa. For a work visa you would need to independently (i.e., separate from your investor application) meet the requirements to qualify for a work visa, e.g., sponsored by an employer in New Zealand. You can find the documents required through checklists on the Immigration NZ website or through local receiving offices, such as VFS in your home country.