I'm currently using Coinjar and they are pretty decent. I think their fees are the lowest. 1% on each transaction. You can also get a swipe card later. However they do not support all banks for deposits. Commonwealth and Westpac are fine but you can check out the full list on their website. You can deposit through wire transfer, POLi pay and Bpay. They also do not support other altcoins, so what i do is transfer my coinjar bitcoins to other trading platforms like Bittrex to trade Bitcoin to Eth for example. But anyway, i would recommend them.
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CoinJar is well known however a 1% trading fee is no longer competitive in the market. You can find better better crypto exchanges in Australia that offer fees from 0.5% This means you get more Bitcoin for your Dollars. Google Swyftx and Independent Reserve.