I ended up applying to my own bank for a credit card, because I thought I would not have any trouble obtaining one from them as I have been with them since Kindergarten.
I applied for a
World Vision Visa Card from the Commonwealth Bank. Apparently whenever I spend money, the bank donates a certain portion to World Vision.
It costs me $30 a year. There is an interest free period of 55 days, so I always pay off my account before then.
In the four or more months I have had the card, and after the $2700 odd payments I have made with the card, I have only had to pay $0.07 interest, and that was because I withdrew cash from an ATM.
Interest rate is something like 5.99% introductory and 16.99% after that.
If you are capable in managing your finances, and won't be tempted to spend to your credit limit, any card with a high interest free period is good.
If you think you will be too tempted, go for a card that doesn't have a high interest rate (those new Aussie Credit Cards perhaps).
If you have a good banking record with your current financial institution, try applying with them. My income and other figures I applied with weren't very impressive, yet they accepted me and with a $5000 limit.