I don't understand the reluctance to purchase tickets thru sites like Expedia or Travelocity. They are online travel agents and as such are better placed to book multi airline itineraries. Airline websites only offer their own services & perhaps some codeshare, which is fine for simple itineraries.
If you miss a connection it is handled the same way as if you booked it directly with the airline, it makes no difference. All bookings end up in the same system regardless of how and where they were made.
Last year I went to Dallas via FRA on the way out and back via EWR, the connection from DFW to EWR was cancelled due to a technical problem. I had booked thru an online travel agent because this is what my company requires me to do. At the airport CO treated me the same as everyone else and rebooked me onto a direct AA flight back home.
As for connections, the legal connection time is built into the website and it is impossible to undercut it, unless you do what some do on this forum, which is to book flight sectors on this website and that website and have separate tickets issued from various websites. This is problematic if you miss a connection, you are on your own to sort it out.

Odin is correct, even though it was not mentioned that the flights, as always, must be on the same PNR. If on separate PNRs the airlines are under no obligation to help with recovery from another airline's problems.

Not also that online agencies have been known to put multi airline itineraries on multiple tickets from time to time. That would be problematic in the event of service recovery. Thre are stories around here of people buying a complete itinerary and it ending up on multiple ticketss.

Local travel agent are able to do the same bookings as the OTAs and it may very well be worth a fee to have them handle it while you sit and watch and can assure a single ticket.

Another area to watch is luggage forwarding. Some airlines no longer will transfer bags on to the next, even if the bags are "checked through." We once flew Christchurch to Seoul with a change of airlines in Auckland (Air NZ to Korean). ANZ would not transfer the bag to Korean so we had to wait for the bag and drag it across the airport (one could also take a taxi) to the international terminal. This occurred even though they have an "interline" agreement but now the two airlines were in different alliances. So be sure you would not be vulnerable to such air tantrums.

Thank you both.

My reluctance is fear of the unknown more than anything. I don't want to screw up someone else's ticket by not knowing what I'm doing. The more I know up front, the better.

So how do I ensure all flights are on the same PNR if booking online?

I often fly on separate tickets from Australia to the US - not because I choose too, but because it's impossible to get a Singapore Air ticket with a UA connection issued on the same ticket (even though part of the same alliance) - even the travel agents here can't do it - unless it's a RTW ticket. I don't understand why, but in five years of trying, we've never succeeded.

Haven't tried through a booking site though, maybe that's the answer.

Seat pitch and seat width for the 777-300s:

Air NZ
Economy Class 32.0-33.0 17.1

Virgin Australia
Economy Class 32.0 18.5

One-stop trip vs a 2-stop trip with 1.4" wider seat on the long haul.

They're both two stops - LAX and Auckland for Air NZ, then a connecting flight to Queenstown.

LAX and Brisbane for Virgin Australia, then a flight to Queenstown.

I've also found some flights on Qantas on the 380 LAX to Sydney, so yet another possibility.

I think I'm convinced I need to give a booking site a go though, as just easier all around.

Odin says above -
"I don't understand the reluctance to purchase tickets thru sites like Expedia or Travelocity."

Maybe because -

From current thread by halemu -
"I purchased tickets thru Orbitz for a trip to Europe and found a letter had been deleted from my last name - not only could Orbitz NOT change the spelling, but I was charged 350 per ticket to cancel them, so watch those spellings carefully!! "

regards - tom

Then again...