I've tried about everything, and have settled on riding first, outside or rollers, preferably ending at the gym, where I do one set of 30 as follows: Leg sled, seated rows, hyperextension machine, free weight squats, free weight benches, situps with thighs at 90°, and one-legged calf raises. I do them all with enough weight to work almost to failure, except for the hyperextension machine where I just set it on max. No resting between exercises. This weight workout takes about 20 minutes. If I'm riding outside, I ride home afterwards, including a couple of good sprints. My schedule and ability to absorb training has me doing weights twice a week. I quit the gym when I start doing serious intervals in May.

The effect of this is to build all-round fitness, rather than to strengthen particular muscles. Note that there are no single joint exercises, or anything that might possibly cause knee or back injuries, and that gym time is minimal, concentrating on the biking time. This works for me. Your mileage may vary.

This program does not cause me to gain much lean muscle mass, though I do gain strength. Maybe that's just me. I also notice that as the weight I'm able to use increases over the winter, so does the cog I use when I do the longer local climbs. So my wattage at LT goes up, which is the whole idea. My understanding of the theory is that when more of your muscle fibers are recruited, you will use a smaller percentage of them at LT. Thus they will fatigue more slowly and you will do better on long climbs and climbs late in the ride.

I must be in the untrained category, as I'm time limited to only about 5000 miles/yr. Certainly not an "elite" cyclist. So I find more leg strength helps my climbing and sprinting, and my ability to maintain a fast cruise. Core strength prevents injury and being forced off the bike by pain.