Just in case anyone here rides or knows someone who does... What's the best and cheapest way for me to pass a motorcycle Basic Handling test? Should I buy a cheap-ass bike or go to a bike school and learn? (I'll definitely buy my own bike once I've passed basic handling.)

Ok, If you have no previous experience with bikes definitely fork out for the bike school, they teach you valuable information on how to not die when riding. Otherwise if you can ride it ok, eg change gears, indicate, stop, just buy a bike and keep practicing up and down the street.

hit www.kiwibiker.co.nz

As for buying a bike, buy a reasonably ok one to start off with. I would suggest a 4 stroke as they dont have the violent power bands that the 2 strokes do.
Go for a 250cc, it may be a bit more expensive but the power is there if you need it.