Natural Marksman, I am a fellow Aussie and a former member of the Australian IPSC team, so my bias is towards the action shooting sports and against the slow fire style competitions.
The basics are the same in each state:
1) Join a pistol club
2) Pass a police criminal record check.
3) Complete a club training course
4) Apply for a probationary pistol license
5) Wait six months
6) Buy your first hand gun. In the first year you can only own a centrefire or a rimfire, not both.
7) After 12 months are up you can then purchase further guns, if your club will sign off on them being required for a given competition.
In that six month period you should borrow or hire as many guns as possible to find out what works for you.
Before joining a club you should decide what type of competitions you want to shoot. If you like the zen moment of trying to hold completely still and shooting between heartbeats then ISSF style shooting is for you.
If you like big booms and recoil and being out doors then IHMSA/IMSU metallic silhouette shooting is for you.
If you like the idea of running full tilt through an obstacle course while hammering down steel plates and shooting moving targets then IPSC is the go.
If your knees are giving out but you like the idea of IPSC then try Action Match. It's IPSC without the movement.
If you like the idea of IPSC but want to shoot a revolver try ICORE.
If you liked playing cowboys and Indians as a kid then look at single action shooting, it's dress up games for adults.
Some links:
www.pistol.org.au for ISSF shooting.
www.ipsc.org.au for IPSC. Check the links page to gun dealers. Also check out the IPSC forum at:
http://www.ipsc.org.au/phpBB3/
http://icoreaustralia.org.au/ for revolver shooting.
http://www.actionmatch.com.au/for action match
http://www.ihmsa.org/ for silhouette
http://www.ssaa.org.au/ with lots of useful links.
My pick of firearms that you can obtain in OZ are as follows:
CZSP01 Shadow. Very accurate, cheap. Ideal for IPSC production division.
Bul M5 or STI Edge for IPSC Standard Division.
S&W 686 for any slow fire centerfire match.
S&W 627 for ICORE.
All of the above should be able to to group 5 shots into an inch and a half at 25 meters.
Good luck.
Ken