I would like to choose bank accounts that offer good interest rates and convenient services with minimal fees. This can help in saving money to buy a good home later. ;)
Online Savings Account
Ratecity (referred to from ASIC) is a financial comparison website in Australia that makes it easy to find the best choice of bank accounts available. It points out that there are online savings accounts that yield very good interest rates, such as USaver (backed by NAB so should be trustworthy) that yields 6.51% p.a. if you deposit >$200 a month into the account. The interest rates of online accounts are very attractive, but the problem of these accounts is that it doesn't provide the usual conveniences of drawing money from ATMs etc.
Typically one would need a transaction account that gives you ATM access, EFTPOS, cheque facility, etc. I do not see significant differences between the transaction accounts, so I'll likely just choose one from the big names such as nab Classic Banking. These accounts pay virtually zero interest, so I'll probably set up my payroll to go into the online account directly and then regularly transfer enough money to the transaction accounts (note it takes a business day for the transfer to go through).