I'm 13 hours into a RA-Aus course myself.
You want to do your training on a RA-Aus registered aircraft (24-XXXX) as these are cheaper to run and therefore hire.
You also want to do your training from an airfield that you don't need to wait for permission to taxi, etc. You definitely don't want to have to fly to a training area 10 minutes away or have to pay landing fees, etc.
You'll more likely find RA-Aus school that can offer this.
You then learn to fly, get radio endorsement, get passenger endorsement and conduct navigation exercises all in a RA-Aus aircraft whilst studying for your RA-Aus pilot certificate. With your certificate you can fly in command of a RA-Aus registered aircraft in class G airspace with 1 passenger.
While learning with your instructor you are logging DUAL hours. It's these that don't count for much later on when getting RPL/PPL. Once you go solo you begin to log hours as Pilot In Command - these count.
You then take your RA-Aus pilot certificate with passenger, radio and navigation endorsement and ask for an RPL. You will have all the flight experience already except you will need to do 2 hours of instrument flight in a VH-XXX registered plane and whatever training is necessary to be proficient in controlled airspace procedures. You also need a medical. You can then fly anywhere in Australia with passengers in a VH-XXX or 24-XXXX aircraft (weight restrictions and aircraft type restrictions apply).
You then take your RPL and ask for PPL. You will have to do more exams. You'll probably just build required hours through normal flying. You can do further training for night flight, instrument ratings, particular aircraft type ratings, etc.