To add to matthandy's post:
The cheque, savings or credit question when buying something relates to credit cards offered by the big banks. When I lived in Aus I had, through the ANZ, a Visa credit card, a savings account and a cheque account all on one physical card. I could then choose which account to pay from.
For debit cards it's less of an issue as typically the credit and savings options are linked to the same account, but most debit card accounts in Australia have a limited number of "savings" transactions that can be made each month, where "credit" transactions are usually unlimited.
As for cars, yes, all European cars are much more expensive, except things like the Astra which Holden bring in and rebadge. As there is a strong domestic car market, all the European brands are taxed heavily. Add in shipping and you're better off just buying a Commodore or a Falcon - there's a reason those cars sell so well. They're the size of a 5 series BMW and cost AUD40k (admittedly the quality isn't there, but if you have kids, it's a big consideration)
Definitely apply for LAHFA if your employer approves it, it will be worth a great deal to you.
I lived in Sydney for many years and if you'd like any other more specific advice about areas to live in or some such feel free to drop me a PM. All the best for the move.