Car or Campervan
Because of the vast distances between major destinations, sitting on a bus for a ten hour journey is common and can become a dreaded necessity of travelling in Australia. Covering these inevitable long hauls in a car is far more enjoyable and allows for stops in remote places along the way whenever you want. Despite the whining done by Aussie locals, fuel prices here are among the lowest in the world at about $0.85-0.95 per litre, make driving reasonably affordable. If you get ahold of a campervan, you can cuts costs even more by sleeping in it.

Buy
Owning your own car brings with it the freedom to be able to go where you want, when you want, but also comes with the risk of breakdowns and the hassles of paperwork.

Noticeboards in hostels, internet cafes, and backpacker companies are a great place to look for wheels. Most ads will have a photo, contact number, price and all the relevent information about the car. Many cars and vans will come with a loads of camping gear that people leaving the country will no longer need which will come in handy and increase your freedom as you'll be able to sleep pretty much anywhere. People who advertise their cars on noticeboards will generally be willing to negotiate their price.

There are companies (such as Traveller's Auto Barn) which sell all kinds of cars, 4WDs and campervans with a guaranteed buyback promise. This might be a safe bet as far as getting a car with the proper papers and will take the hassle out of worrying about selling your car at the end of your trip, but they'll charge more than the average punter a car via noticeboards.

Cairns, Sydne and Melbourneare the best places to buy a car/van because people tend to buy cars to drive between these destinations and sell them when they arrive, so there will be loads of choice. But cars can be bought and sold fairly easily all over the country, even in small towns.

You're going to want a car with enough registration left on it to cover your travels as it can be a huge hassle and very expensive to renew. You'll also have some problems selling your car at the end of your journey if you don't have at least a few months rego left on it. Make sure registration is transferred into your name to avoid being held responsible for the previous owner's parking fines and tickets. It doesn't take long to fill in the form and in most cases the previous owner will have all the required paperwork for you when you make the transfer.

Insurance is included in the price of the rego but only covers people hurt in an accident and nothing else. Third Party Property insurance covers any vehicle or property (not including your own) that you might have damaged and can be purchased from Traveller's Auto Barn or King's Cross Market among other places.