New Zealand is due for a new Governor-General sometime next year. Unfortunately, we don't get to choose them - the decision is entirely in John Key's hands. But we should be able to. And the Republican Movement is highlighting the democratic deficit in our highest office by running its own selection process online.
You can nominate people here. Presumably, they'll be publishing the list and running an "election" for it - exactly as should happen in reality (though given the nature of the office, I'd be happy enough if Parliament chose them by a supermajority process).
As for who I'd prefer, I prefer former judges as Governors-General for two reasons. First, they know the constitution. And second, they know their place. The role of the Governor-General is to host dinner parties, sign whatever is put in front of them, and keep out of politics. Judges seem to understand this well. Former politicians don't. Unfortunately, given National's approach to important constitutional offices, the odds are they'll choose one of the latter.