I think commonwealth Bank normally has the lowest rate. Otherwise, check out the Credit Union. Other than that, some internet banks provide quite low rates, but I would worry about the credibility. We always go with NAB, since they don't charge us the application fee (normally 600), and the process is very easy after we did once with them. Nowadays, most bank do not charge application fee if you borrow a lot. Also, if you do not repay very quickly, the application fee does not weigh much in comparison with the whole repayment.
We don't worry about much about the rate, because we repay quickly (one or two years). I suggest that use the calculator to compare the package which the banks presented to you. Whether you will take the honeymoon rate for the first year (if you repay a lot in the first year) or take split rate (half fixed and half variable), really depends your plan of repayment. I don't think the rate would go up quickly in future, so fixed rate (they would limited your repayment each year/ reduce the principle is always more important)would be out of questions.