Welcome to the forums.
To my knowledge, (not sitting in front of the game at this moment), there are 2 ways to see the different units you can build. The 1st is the left/right arrows on the right side of the build list (this will move the list left or right). The 2nd is the mouse wheel (it will also move the unit selection left or right). Have your tried both, and do neither work for you?
Remember - The beatings will continue until morale improves.