While it used to seem that mosts cyclists didn't want to spend time in the gym because they incorrectly thought it would add un-needed weight to their body or they thought the time would be better spent on the bike I can tell you that the trend is towards using the gym to improve cycling and acheive total fitness especially for the master age athlete. I recommend that cyclists incorporate weight training not just in the off-season but year-round. There is little point in starting a weight training program in December just to abondon it in March. With this system you spend weeks every winter acclimating your body to the training just to quickly lose it as soon as your stop in the spring. Instead, you should devote more time in the winter, maybe two or three days per week, and then taper down to one or two days during the season. The types of exercises, sets and reps would also be adjusted depending on the time of year. I certainly go heavier on my legs in the winter but keep core and upper body in my routine all year.
You should choose weights that allow you to complete 2 or 3 sets of 8-12 reps. Usually this would be about 75% of your one rep maximum. I'm not recommending your try to find your one rep max by picking up two 80lb dumbells and trying some curls! A little trial and error will let you find the correct weights. Notice also that I'm talking about free weights and not machines. There are some great machines but they do work isloated muscles. There are some machines like the leg extension, Smith machine, and leg press that I avoid. They present a variety of issues with your back and abnormal motion of your legs but thats a discussion for another day. I prefer to work as many muscles as possible and free weights accomplish this. Here are some exercises that should be a part of your workout routine:
lunges (in place, side to side, backward, etc; don't just work in one plane of motion)
squats (many options from feet together, single leg, legs in lunge position. etc)
pushups (many types from standard to elevated feet to rotation, etc)
sit-ups (many variations)
planks (standard and side)
squat combo: combining the squat with an arm curl to a press
I have a list of over 100 exercies that I use in my classes and with personal training clients. You would be welcome to attend one of my classes at the Cincinnati Sports Club or we could have a team training day there if anyone is interested. Working towards total fitness will help your cycling!