While you should most definitely weight train to increase strength, technique is much more important than strength.
The technique is like a whip, and to do it properly your body must become a whip. To do this you must have correct bai jong positioning and perfect relaxation BEFORE throwing the punch. It usually helps when you tell the person to stay upright throughout the whole punch as many beginners tend to lean forward and overcommit in an attempt to gain more power (which it doesn't). Practising it slowly first will help too.
Remember also that its not about hitting the target HARD, it about hitting it GOOD. Connect!
The biceps and triceps can add power to your punch. The biceps does this because it adds mass to the arm, but funnily enough, if you punch incorrectly, then big biceps can actually have the opposite effect (If they tense, they act as a brake, slowing your arm). The triceps also adds weight to the shot, but most of the benefits of triceps strenghtening come from the increased force that can be applied in extending the arm.
Finally, If you are going to be strength training, you should train your whole body. Work on the larger muscle groups instead of focusing on arm strength. Compound exercises are the key here. You'll gain muscle and strength faster and your smaller muscles will also be worked as hard as they need to for now (e.g. while a chinup targets your back, your biceps will also get a heavy workout) There should also more good information in the strength training forum.
Sticks n stones'll break my bones, but if I land the first one, you're in trouble!