Westpac for me. Very accomodating for the person moving overseas, superb customer service, lots of branches everywhere.
As for phones, it depends whether you are bringing one with you. If you are, 2 degrees is a no brainer (quite simply - it's the cheapest but pretty much has as much coverage as anywhere).
If you AREN'T bringing a phone, well, unless you want a very basic phone/cheap smartphone, you'll have to use Telecom. Every other provider is ludicrously expensive.
On a $100 per month plan (all networks give approx same deals), you get an old LG Optimus on 2 degrees, something like a Samsung Galaxy Ace on Voda - and an Iphone 4s on Telecom. They also did the Galaxy SII for the same price in Jan. In fact, I presume Telecom have bought too many Iphones (not surprising - Apple set the price and the volume, and there's no negotiation), as their current prices for all models are easily the cheapest around - much cheaper even than the UK's cheapest provider, 3 mobile.