Yeah, bulking up should be the first of your worries. Then, when you want to bulk up your forearms and (try to bulk your) wrists, you should try this two things:
Hammer Curls:
Either with a specialized barbell or dumbells, curl your arms like you would with a normal curl, except keep your palms facing each other throughout the movement.
Wrist Curls:
Sit down, and rest your forearms on your legs. Your hands and wrists should be hanging down just in front of your knees. Now, with weight in hand, curl your wrists towards the ceiling. Try this with both your palm facing upward and with your palm facing downward.
The wrist, though there are many muscles there, doesn't bulk up easily (or at all in most cases). So don't stress if you can't make them bigger.