Hi Kayleigh
Welcome to PIO! I've been in Sydney just over 3 months now and loving it, I've also been using this site to meet new friends here! We've just arranged a meet up for the girls in Sydney round here and hopefully we'll make it a regular thing, so once you arrive you're quite welcome to join us all. Or if you fancy a coffee or whatever I'm always up for meeting new people! Do you know whereabouts in Sydney you'll be?
As for your queries I found that the pay as you go options with Vodafone over here a great value, and mean that you're not tied to a contract. I got a bog-standard phone for the equivalent of about 35 pounds. If you credit your mobile with $30 (about 15 quid) you get a choice of freebies, for example I get 60 free texts and 100 minutes to Vodafone mobiles after a 20cents connection fee. This kind of credit normally lasts me a month or so, definitely a lot less than I was spending per month on an Orange contract back home!
Bank accounts I found a bit strange when I arrived, there is generally a monthly fee ($3 in my experience) for the privilege of using ATMs, and even then there is no 'LINK' system so you can only use the ATMs for your own bank for free. Other than that though I think there are less fees etc so I guess it rounds itself out. I'm with the NAB (National Australia Bank) and haven't had any problems, but I'm sure there are plenty of other PIO members out there who have been here longer and will be able to give you further advice about banking here.
I hope that's helped a little bit. Feel free to PM me if you want any more help, or if you just want somebody to chat to

All the best with the move!
Rachel