Weight-lifting. How much, how often, and what exercises?

I read somewher here that it was good to build up your tricep muscles, since they are the muscle group that does the pushing action, while biceps do the pulling action. My biceps are good enough, how I wanted to know from your guys' standpoint if it is good to build up the tricep muscles, or if building them up will slow you down. I'm not doing heavy lifting, just 40lbs. 3 sets of 20 reps doing tricep pulldowns on an exercise machine. I know that some people say in boxing that it isn't smart to weight lift because it slows you down, but I believe that it can make you faster and stronger, which is entirely based on not using heavy weights and doing lots of reps.

My last question is what should I try to focus on most when doing light weights, the shoulders or the tricep muscles. I'll leave it at that. If you guys could answer my question, I'd appreciate it. Thanks!