First off, you will need at least a Silver recreational license before you can start riding track. CA have a 3 month silver license for $29 for new people. Don't buy it yet. Wait until just before you start off to buy one. It'll last you until the end of the track season(~March). And if you really enjoy it, you can upgrade your license in October(to get an extra 3 months for free) when track starts again.
Dulwich Hill Bicycle Club(DHBC) is your closest club, one of the biggest in NSW. Their track sessions are on the site:
http://www.dhbc.org.au/#track" onclick="window.open(this.href);return false;
Their velodrome is right next to Tempe station. Go to the track on one of their training nights and have a chat with them. They'll let you know all you need to know. They've got loaner bikes to use.
Lidcombe-Auburn Cycle Club (LACC) holds training on Wednesday evenings at 7pm, and racing on Fridays at around 7pm.
Their site is crap:
http://lacc.org.au/index.php" onclick="window.open(this.href);return false;
But at least their FB page is updated regularly:
https://www.facebook.com/Lidcombe-Aubur ... 187953546/" onclick="window.open(this.href);return false;
Bankstown Sports Cycle Club(BSCC) uses Dunc Gray Velodrome(DGV), which was the Sydney 2000 Olympics venue. During Spring/summer season, they have track racing on Wednesday nights. When it's winter, they have training(160 lap pace lines I think) on Wednesday nights.
Site is pretty messy, but info is there:
http://www.bankstownsportscycling.com/track.html" onclick="window.open(this.href);return false;
FB:
https://www.facebook.com/BankstownSport ... ts&fref=ts" onclick="window.open(this.href);return false;
St George Cycle Club is probably the most race oriented club. They use Hurstville Oval. I've never been there, so I don't know what it's like.
http://www.stgeorge.cycling.org.au/defa ... Page=50147" onclick="window.open(this.href);return false;
There is also a track in Merrylands, however, this one is in bad shape, and isn't used for racing anymore. I believe it was the Parramatta club who did use it a while back.
Don't worry about the getting a bike yet. Get out there, hop onto one of the club loaner bikes and see how you like it first. You learn as you ride, and there'll be someone leading you out most of the time especially when you start off.
Also get in touch with the clubs before you head to one of the training nights. Being Christmas/New Years now, some clubs don't run training sessions for a few weeks.