Best way to sign up for SkyTeam?
It depends on how much flying you do and how likely it is you will fly on a SkyTeam airline.
I am an NZ Gold Elite as well, with most of my flights being Star Alliance or OneWorld (I'm QF Gold).
Given that I don't fly on SkyTeam often it is unlikely I'll get status with them. So I looked at three options-
Garuda: about to join and one if the airlines in the region;
China Southern: Fly to New Zealand and one I fly with a little bit. Points expire after a few years, from memory.
Delta: US based, points don't expire.
I ended up going with Delta simply because their points don't expire and I can't guarantee I'll fly enough with SkyTeam to get enough points for a reward flight on Garuda or China Southern before they begin to expire.
Of course, if Virgin Australia was to ever join (not sure it is likely) I would switch to them pretty quick!