If you're going to look for work in Australia then you'll need to set up a bank account for your payment. If you're sure the jobs you do will be cash in hand then you won't need one, but otherwise it's a good idea to do it.
I went with Westpac but a lot of travellers I've met have also gone with Commonwealth. I went with Westpac because that's who my family here are with and it was just easier for me to open accounts with them too.
It's just a case of taking your passport and proof of visa to open the account. You may also need your tax file number (TFN), which you apply for online. I didn't have that (and I didn't have an Australian phone number either) but I opened the account and emailed the personal banker once I'd sorted them.
I went for a standard 'Choice' account (a current account, if you're British), a savings account, and a Super Fund account. This is something that was recommended I do by someone with a Finance degree in New Zealand, and when I asked in the bank if I could do it the banker said "Ooh, you've done your research." So I think it's something you should do!
Basically a Super Fund is like a pension fund, that your employer will pay into every month. You can reclaim this money when you leave, minus a proportion of it that is taxed. But it's a good idea to open a Super Fund account because if you have multiple employers during your time in Australia then they'll pay it into a Super Fund account of their choosing and you could end up with several, and then it's easier to lose track of them and ultimately end up losing money.