Shel is right they will just presume higher risk but, as long as you have papers showing that u have income they will lend you. Not sure if interest rates would be higher or same.
As for bank, we chose CBA, it was very simple. They have a migrating to Australia section which shows the steps on their website. You can create an account and transfer money and once you land in Australia, you show them your ID at local branch and they will give you debit cards and you are ready to spend. Also the account fee is waived if you deposit at-least $2k a month.
I didn't check other banks but I assume they have the same scheme.