The advantage of DL is that points don't expire but be sure to check their new earnings charts. The mainland Chinese carriers such as CZ and MU generally have poor FF programs. I also would avoid Garuda and AirEuropa as FF programs.

Some SkyTeam carriers have bilateral partnerships with VA, which could work for someone in NZ. Check whether your flights can earn points on VA = Virgin Australia. This also means that DL miles can be used for VA flights, but the same is not true for all SkyTeam FF programs. You should be able to credit AirEurope to DL and then use DL miles for VA flights. This could well be your best option as NZ based.

AFAIk you can sign up for any FF program online for free, although they might not send you a card until you have some miles.