When choosing a heater for your home, the type of fuel it uses is of utmost importance. If you want a fireplace, for example, you need access to firewood. If you want a gas heater, you need a connection to a gas line or a gas tank. And while sunlight is available throughout most of Australia, in the places where serious heating is required, the amount of sunlight that's available throughout they year might not be sufficient to provide cost-effective solar heating.
What's available where?
In some areas, some fuel types are simply not available or practical. Many homes in Australia don't have access to gas piping (often called gas reticulation). In that instance, it's normally necessary to opt for either an LPG system or an efficient electric heating system. Some in rural areas have unreliable supplies of power, making electric heaters a sketchy option (unless they have solar panels to supplement their mains connection). In that instance, LPG is a common option, but firewood is also in plentiful supply outside of the city too.
Think of the future
You also need to ask yourself if your fuel type will still be readily available in five or ten years. A coal burner, for example, while rare in homes wouldn’t be a smart long term option. Likewise, electricity prices are rising, and will continue to rise for the foreseeable future. If you're considering an electric system it might also be a good idea to think about what it might cost to install solar panels, and what types of rebates you're eligible for.
Tradeoffs with different types of fuel
There are various trade offs that you need to keep in mind when weighing up fuel sources. Wood is obviously available nearly everywhere, and in rural areas in particular a fireplace or wood heater makes good sense - but with most wood heating systems you don’t get the same heating output as you would with an electric or gas heater. Organic pellets have similar availability but similar problems to firewood as well.
Likewise, wood heaters are relatively high maintenance when compared to other systems, and require occasional cleaning to ensure that they run as intended. If you only need to heat a home for a few weeks a year then this won’t matter at all, but for homes in cold climates, solid fuel burners will require regular cleaning.
Gas or electric?
If there is gas reticulation available in your area, it's likely to be a more affordable option to electric heating. Likewise, gas is a relatively clean fuel source in terms of greenhouse gas emissions. Electric systems are the easiest to operate and most convenient as far as portable heaters go, but the ever-increasing cost of electricity means that electric heaters are almost always the most expensive to operate. The other advantage to gas is that even if the power goes out, your heating will stay on.