I don’t know how much ‘pre study’ you have done but there are a couple of great YouTube videos on operating the car that I have linked in the past to help people.
The actual pick up procedure is pretty slick and they are keen to get you out the door. There isn’t time to have a thorough look over the vehicle there and then. There are delivery day checklists (and even apps) available online. In my case I looked for any obvious damage before accepting the vehicle and drove out of the delivery area (which is inside) to the car park where I looked for major defects because you have a week to report anything. If your pick up day is anything like the weather is today in Auckland, good luck with looking at it outside!
Make sure you’ve got the Tesla App loaded on your phone and logged in.
Once you set off it will take a number of kilometres for the cameras to calibrate and the autopilot functions aren’t available until that is complete (I think it was about 10-15km for me).
Not sure how much of your ‘emergency equipment’ you are taking to Auckland with you. I was lucky because my home is within Tesla service area if something went wrong on the drive home.
Shouldn’t get excited by something like a car, but you know………..