Welcome to the forum Emms. Question for you: do you travel on your British or New Zealand passport? It'll make a difference if you want to live and work here. If British then as a EU national you can just turn up and apply for a residence permit, funds permitting, and then you can look for a job. If you use the New Zealand one though you need to get your permit pre-approved by the Swiss authorities first.
"Nationals of the following states do not require a visa to enter Switzerland under any circumstances: Brunei, Japan, Malaysia, New Zealand and Singapore.
However, the competent Swiss authority will issue a prior authorisation of a residence permit in the following cases:
a) for a stay of more than 90 days, or
b) a stay involving gainful employment:
lasting more than eight days, or
from the first day of work in the primary or auxiliary construction sectors, the hospitality sector, industrial or private cleaning services, surveillance and security services, itinerant sales and services or erotic services.
This prior authorisation of a residence permit is issued directly to the foreign national, or to a third party (employer), by the cantonal migration authority. The Swiss diplomatic or consular mission is not involved in this procedure." https://www.eda.admin.ch/countries/m...ency/visa.html
You'd need to apply to the cantonal migration office of the canton you plan to live in to get pre-approval.