Opening a bank account is essential for living in Australia long term. You will need a bank account to be able to access some services like getting a phone line or renting a house, so it should be one of the first things you do when you arrive in Australia.
Do some shopping around, however, essentially most banks offer the same services including, online banking and Automatic Banking Machines (ATMs).
When opening an account you will usually be asked for a few forms of identification and proof of address. As a new migrant you will also be asked to provide a reference from your employer.