I am certainly no weight training expert, but I did spend time researching the subject late last year as I was particularly wanting to do weights as part of my training this year.
From a cycling/ racing performance point of view, the consensus seems to be that you need to be doing heavy lifts for the legs, so squats, deadlifts, step ups, leg press, leg curls etc. of course to a lesser degree the upper body needs some work but not the heavy lifts and of course some core work.
I started by reading the weights section in The Cyclists Training Bible by Joe Friel, Weight Training for Cyclists and by reading material and videos on the internet.
You may know all this already of course but the way I programmed my lifting was to divide it into 4 phases
Anatomical Adaptation
Transition
Heavy Lifts
Maintenance
The AA concentrated on getting the body used to lifting, so start with a weight that you can complete 20+ reps on and maybe 2-3 sets of each. The AA phase lasted about 3 weeks and you slowly add weight but maintain the high reps. Then legs moved on to the next phase but upper body remains in AA.
Transition is where you start to increase weight towards the heavy lift and target perhaps 10-15 reps with 3 sets of each slowly increasing weight each session in the gym. The transition phase should last about 2 weeks.
Heavy Lift should target 3-10 reps, once you can do 10 on the first set then increase weight.The heavy lift phase should last about 3 weeks
There is another phase you can do after the heavy lifts that I forget the name of but it is where you go for explosive power so focus on fast reps on the legs.
Maintenance
As you get into the build phase you will want to drop the lifting to specialise HIIT on the bike but a once a week maintenance lift is often recommeded with lighter weights.
2 or 3 times a week is suggested, I started out going to the gym 3 times but this ended too much so I reduced to twice a week.
Lifting should replace High Intensity work on the bike.
Here is what exercises I was doing. I stopped going when Omicron arrived as the gym seemed like ideal breeding grounds. By the time I was willing to go back I considered it too late to start again as I was focused more on the bike. Maybe I will start again this November.
Squats
Lat pulldowns
Leg Press
Heel Raise
Single arm row
Dumbell shrug
Leg Curl
Seated Row
Bench Press
Abdominal twist
Abdonimals straight
As far as stretching is concerned I do tend to neglect this a bit but try to do just 4 simple stretches
Calf, Quads, Hamstring and Glutes
) Strength Training for Cyclists: 10 Exercises for Cycling Weight Training - TrainerRoad Blog