What do you mean by quite a while? If it is going to be a long time (ie. 6 months or so), you will probably want to consider buying a car. There are cars in any price range pretty much, although the cheaper ones will also be less reliable - which can really hurt if you break down in the middle of the desert! Definitely consider geting RAC coverage if you buy a car; they'll help you out if you break down somewhere. If you're not here for longer than a few months, hiring a car may be the way to go - sorry to say I've never hired a car here though (apart from a moving truck once :))
Where are you planning on driving around in Australia? I'm no car expert, but if you just plan to go down the east coast and pretty much stick to major cities, pretty much any sedan or small car would do (might want to make sure it has air conditioning if it's in summer though). If you plan to do some off-roading or head out bush, you may need a 4wd. I can't really speak for NZ. Let us know some more details, so we can help out more
