You have many different options of aeroplane experience.
You can choose recreational flying (RA AUS) on two seats aeroplanes, which is the most economical way of getting yourself into the air. Initially you may be somehow limited by the size of aeroplanes and airports you can fly into, however these limits can be lifted by further airplane lessons. Should you wish to surprise someone a lesson in one of these would be a great gift. Generally student finish their recreational pilot license first, before they convert to bigger and more complex airplane. However you can convert at any stage of your training. Overall RA AUS is a fun way to an adventure and a useful skill. Perfect way to take your loved one for a trip to local islands visit a friend on a farm or simply enjoy the pleasure of being free in the air. You have a choice of being a part of a club or you can attend an aviation school. Clubs are generally more friendly and also include socialising. Commercial schools on the other hand are better organised and get your results faster. There does not seem to be much of price difference between the different types of training.
Private pilot license (PPL) is a fast track to aviation without any limitation. Generally it is more structured course due its complexity and required standards are higher at earlier stages. It cost more than, RA AUS due to more expensive aeroplanes, their servicing and higher landing charges. There are two ways to get this license.
Club orientated schools are often cheaper and combined with social activities. Such clubs are all around Australia generally away from the main airport. Generally they very friendly and budget minded. Frequently whole families are part of such clubs and they are operated by volunteers. Their activities are very wide and extend to various celebration, fun and games involving people from non pilot background.
Commercially operated training centres are generally more organised and have better structure. They are goal orientated, so higher cost is offset by flexibility and availability of aeroplanes, instructors and training material. Most of these will guide you quickly to your private pilot license (PPL) and many can train you to commercial standards for commercial pilot license (CPL). Commercially operated aviation schools are frequently the fastest way to achieve CPL or even higher standard license.
PPL pilots are allowed to fly various size aircraft to most places, however PPL license does not allow you to charge for your services and you can not be employed as a pilot. CPL pilots are trained to higher standards and can be employed as pilot. They can also work as instructors or in other aviation positions. Such high aviation standard is mostly achieved via professional aviation schools.
The best of all worlds may be combining all of the above. You first flying lesson should start with RA AUS aircraft as it is the cheapest way to get yourself in the air. You will have the same lesson experience from a 2 seats aircraft as you would from standard general aviation (GA) aircraft. Then you can decide which direction you wish to go. One way or another your first lesson, no matter what it had been flown in, can be used as part of your initial training. A lesson gift for such experience is a great birthday present.