Squats, leg presses and so on will increase your fast-twitch response - good for jumping away from the pack on a break. Too many though will make your legs very big. If you want endurance, just keep riding your bike.
Lots of cyclist suffer from a strength imbalance - powerful legs, weaker torsos and upper bodies. Core strength i.e. abdominal and back strength, is often lacking. Core strength is important for holding you upright, and especially important for runners as it helps reduce fatigue on long runs.
If there is no specific issue that you want to put right with your legs, then I'd use your weights time to work the upper body, and include plenty of sit-ups and back raises.
The only way you will get very big legs,is if you used heavy weights,and train and eat accordingly.Lighter weight and higher reps will help strength and fitness in your muscles.To help your knees you need to do some leg extensions,and leg curls for behind the knee,very light with the weight,and high reps,ie ten to twenty,and smooth action,no jerking.
Not after hulk legs....just toning. I think the 'behind the knee area' is weakest when I haven't ridden for a while....which makes sense....they didn't hurt that much today........hopefully they'll hurt even less tomorrow.
I like the leg curls idea. Those leg curl benchs are cheap enough too....plus I already have loads of loose weights.
Even without any weights on the leg curl,it will help strengthen the back of your knee,just do lots of reps slow and smooth,and the same with the leg extension.If its too easy,as in you can do thirty and its not even starting to feel hard,then put a five kg disk on each side and go for around the twenty mark,but remember that rest is just as important as training,and only do it every other day,do three sets of fifteen to twenty each time,with about two minutes rest in between sets.You will soon find that the strenght in your knee will pick up.Once its easy for you put a little more weight on,another two and a half or even five kg if you feel like it,and do the same reps,just add another set when its comfortable to.You wont get much muscle growth,just stronger toned legs,you need to pack the protien into you to body build,as well all the other ingredients like carbs and fats,and more protien,so dont worry about getting big legs.Your reps would be low,like six to eight and you would need to fail on the seventh or eight rep with heavy weight on.
Used to do an awful lot of weightlifting in my younger days.....at one point I was 14st 6lb.....and being 5'9" I was pretty chunky......since then I gave it all up and also illness made me lose loads of weight...but I have felt fitter for it.....and its only in the last 9 months that I've dropped from 13st 6lbs to a tiny fraction under 12 stone.......but my fitness is even greater still.
The leg curls will really help I think.
It will help if you tailor the weight training to your other sporting needs. I use routines that are based on the effort needed on tough skiing runs and this is very similar to when a tough hill has to be dealt with.