Congratulations on your job!
Depending on what type of visa you are here on, there are a couple of costs you need to be aware of (we're on a 457)
1) schooling costs in NSW. you may be required to pay for your kids to attend public schools. Per kid in NSW: $4500 per year up through year 10, then $5500 per year for years 11 and 12.
2) You might need private health insurance
3) Temporary residents aren't eligable for any spouse/children tax deductions.
4) Temporary residents may qualify for a medicare levy exemption which equates to a refund at tax time of any levy paid.
Again, all this may depend on what type of visa you'll be here on. Sydney is a beautiful city - but expensive.