Strength training isn't a one size fits all kind of thing, especially if you're training to increase your strength for a sport. Today I will use the example of Brazilian Jiu Jitsu since my Husband does it, but the main ideas can flow over to other technical sports.
Whenever I train myself, others, or Husband I only ever do functional, full body, compound, explosive type movements. You will never, ever see me doing a bicep curl, especially on a squat rack :) . When you do other full body movements like chin-ups, or a row, you are using your biceps as well, so it's not necessary to train the hell out of them.
My Husband is a prime example of someone that was a bit confused with strength training. He didn't understand the purpose, and thought that just rolling and doing technique was enough. I agree that you should never stop rolling and practicing technique, but at some point you will realize that it's not enough. Maybe if your legs were stronger you would be able to hold your triangle better, etc, etc. In the case of my husband, his legs are his weakest point, and in his last competition he was complaining how he wasn't able to finish the triangle and that his legs were giving out. Compare this to one of our friends who is 180 lbs of pure muscle who can submit you just by squeezing his legs really hard in triangle. Even I can submit Husband by squeezing my legs together when he's in my guard.
Jiu jitsu guys, you don't have to be scrawny, most of the greats aren't:
Now, look at this guy:
This guy is a bodybuilder. You put him on the mat and he could be submitted in two seconds because he has zero flexibility. He is trained for purely bodybuilding, its not functional for sport. That is why your strength training cannot be the traditional training that most guys are used to: you know, the arms and chest, back and shoulders type thing. What you need to do is explosive full body movements, with some unilateral work to strength individual legs and arms since you won't be using them bilaterally all the time.
Your main exercises:
Squat (only when you're legs are working in perfect order)
Deadlift- all kinds
Clean and Jerk
One legged squats
When thinking, should I do this exercise? Think about how functional it is. Do you actually do this motion in your sport, would a cave-man do it, does it require a machine to do it, is the muscle moving in a way that it would normally? Picking something up off the floor (aka. deadlift) is an important movement, doing dumbell skull crushers or the hamstring curl machine, not so important. I hate machines, but the one I hate the most is the leg extension. At what point in life is your quad moving in isolation without anything else? It's a purely aesthetic exercise with zero functionality. You want nice quads?--> front squat, back squat, lunge, jump, you get the idea
I don't want to give away all the good stuff, so stay tuned on what sort of exercises you would start with to progress safely and prevent injury. Also, be sure to check out next week my interview in Real T.O on 3 sample meals a jiu jitsu goer should eat after class.
One last thought:
Imagine that you are great at jiu jitsu, now imagine that you are just as flexible, just as technical, but now, EVEN STRONGER. Just imagine the possibilities.