OK, so you live in Melbourne, Australia? I assume we're talking about the same 1/20, but it probably helps to list your location when you ask these sorts of questions as this is an international forum and racing varies from country to country.
So: How to get started?
In Australia we ride 'grades' more than 'cats' (though I think some clubs call them cats), and the requirements to move up a grade aren't as formal as with American 'category' (where you need to ride/place in/win a certain number of races to move up). We have A/B/C/D..., in America it's Cat 1-5.
Based on your 1/20 time and your weekly mileage, I'd say you have a good level of fitness, and a solid base to start racing on. You'd probably have not too much trouble in C grade, and might just stick out a B grade race if you had to. However, there's a lot more to racing than being able to get up a hill quickly by yourself. I don't know much about vets racing except that it happens, so hopefully someone else can contribute on that front, but you are pretty fit, and club racing is graded, so I wouldn't worry too much.
To do some club races:
1. Go to a race.
Possible races are -
Hawthorn CC, Wednesday nights, Kew BLVD just off Studley Park Rd above the boathouse, be there 545 for 6. The other clubs also run good races - try Coburg CC on Saturdays 9AM Kew BLVD, St Kilda CC somewhere (sorry forgotten) in Port Melburne Sundays 9AM, or Carnegie CC, Glenvale Cr, Mulgrave, Sundays 9AM.
2. Harass a club official (talk to the ppl at the entry desk/card table) so you can get a three ride licence (about $30-$40, and you can subtract that off your full licence if you choose to buy one).
3. Enter D grade Even though you might be able to finish a higher grade, it's better to win and then go up. This teaches you how to win races (tactics etc), and is good for the motivation too.
4. Fall in love with racing. Buy a full year licence ($140-180 I think).
5. Ride lots, talk to people, learn to race. I think there are a lot of tips on how to ride all over the web and these forums, but most people disagree with each other, and ultimately your tactics will be determined by the type of rider you are. It's up to you to race and learn from experience - talking to more experienced people you've raced with helps too.
6. Periodise your training. Go part time in your job. Obsess about your bike's weight. ๐
Any more questions, post again, or email me on [email hidden] - it's great to see more people getting on bikes and wanting to race, so I'm happy to answer any questions and hook you up with my club officials if you want to talk to them/ask more questions.