I would like to open a small business in New Zealand such as a petrol station or fast-food restaurant.
The relevant category for people wanting to come to New Zealand and get residence through operating a business is the Entrepreneur Work Visa category (EWV). This is the most difficult and complex category for immigration to New Zealand with a decline rate of between 90% to 95%. Unless the business has the potential to provide substantial benefits to New Zealand, such as the employment of New Zealand staff, introduction of new skills or products, or the export of New Zealand products or skills, it is unlikely to be successful.
New Zealand is well served by retail businesses and the types of business you are thinking of are unlikely to be acceptable under EWV category.
If you have enough savings or assets, you might be able to try an Investor category Residence application instead. See our Business and Investment page which contains links to our Guides about this type of visa.