You're on the right track. Doing lots of club riding for a year (or even two) before racing and starting training program early the winter before your first race season is a good approach.
About weight training, it seems most coaches and training programs swear by it. And I have seen it become very popular in the last few years. Nothing is black and white though - I have seen some racers do really well without any weight training.
The idea of weight training is to build strength mostly in the off season, and then gradually as you get closer to the race season, the weight training is reduced, and the strength gained from the weights will increase your power on the bike. It's going from general strength to bike specific power.
During the racing season itself, you can stop weights all together, or keep it to at most one session a week. Some coaches recommend that master cyclists above 40 keep the weight training sessions year round.
I also think that since cycling works a very specific set of muscles, weight training will help balance everything out with other muscle groups.
Core work is also extremely important for cycling. The two major points of contact with the bike are your feet and hands, so core stability is important to maximize power output and reduce fatigue. Climbing out of the saddle requires a very stable core to be efficient. I would keep one core workout session through out the racing season.
Upper body work is important but mostly for racing. In anaerobic quick accelerations, your upper body has to counteract the force in your legs. If you already have a strong upper body, that may not be too critical.
Hope this helps and happy training,