It's pretty easy to move.
When you get here the first thing should do is apply for your TFN - otherwise you get taxed at 49.7%.
Unfortunately you can't apply for it before arriving in Australia.
Look for recruitment companies before you move over and email them your CV and intended arrival date and they can organise interviews and stuff from there. But recruitment companies are really hit and miss here.
The property market/rental/flatting market is a fucking nightmare, I'm not really sure what you can do about this either, it's just shit, but expect to pay more than auckland to live anywhere decent. I was lucky enough to find a friend who needed a flatmate
If you are intending to drive, read the roadsigns part of the road code cause some of the signs here are pretty confusing. Also it's rather expensive to own a car (costs around $800 a year for on road costs).
Take the first 2 weeks off when you come over and just journey around the city using public transport, it gives you a good feel for the place.
NO ONE. I repeat NO ONE with self respect lives in West Sydney, it's crime rate is also rather shit.
Any specific questions just ask me as I moved over here in Jan.