Without a doubt, the best way to enjoy Australia is to drive yourself. It's the only way to make the trip your way, stop where you want, and cover the immense distances that separate everything. The options are, from buying your own car or campervan (van prepared to sleep inside), or renting it. This second option can be more profitable if you plan to travel less than a month, but for longer stays without doubt the ideal is to buy a vehicle of your own.
If you do not mind driving old vehicles, it's easy to get a car for $ 1000 or $ 1500, or vans from 2000 up to $ 5000. They generally recommend buying non-European brands, as they do not withstand the weather and Australian extreme conditions, Japanese and Australian cars being the most versatile and sturdy. Before buying the vehicle it is advisable to check the state of fines (it can be done online), and that mechanically it is well. Old Toyota vans or (exceptionally) the Wolksvaguen Bus hold anything, so they are good choice. Only one thing, you have to be able to cross the Outback without air conditioning or power steering!
If the idea is to buy a campervan or car, keep in mind the seasons: there are cities more fashionable a few months than others, based on their temperatures (monsoon in Darwin, or winter in Melbourne), and there are others that are Extremely popular during the summer in Europe (like Sydney). If at that time there are too many people looking for a van in a city, the cost will be higher, while if you want to sell it when you are out of season, it may be difficult to get a good price for it. We must also remember that it is the southern hemisphere, so it's all the other way around! Summer is winter and spring is autumn.
The best thing about buying a van of this style (campervan), is that they usually come prepared for everything; small generator, tents, chairs and camping tables, a cooker, plates, pans and pans, an extension, tool set ... etc.
By having a van of this style, you can stop at virtually any place that does not have a "NO CAMPING" sign. And then show up at a gas station or on the beach. Most states have well-prepared rest stops, some even with hot water.
Australia is big, VERY big. The distances are very long and there are many things to see, but there are also many hours to drive on empty roads. So it is advisable to bring the gas tank always full, and a small emergency tank just in case (not strange that some gas stations are several days without supply), and bottles of water and food just in case. Several books, music, and lots of, lots of patience.
When planning your route, consider the seasons and rainy seasons: the entire northern area is tropical and suffers monsoons, with abundant roads that tend to flood and rivers that overflow easily. It is not uncommon to be locked up in some village in these seasons, and when the rivers overflow and join the high tide, yes, the crocodiles come out!
Some of the best paradises are hidden, do not appear in the guides and only some locals know them. So if you have enough time, it is good to take the little detours, see each lookout, and lose you among some little villages.