I am not sure what it is you want to show. The best demonstration of precession would be:
Spin the bicycle wheel, hang the bicycle wheel from a string attached to ONE side of the axis. Since the weight of the wheel causes a torque in a plane that is perpendicular to the angular momentum of the wheel; conservation fo angular momentum dictates that motion in the third plane must result.
This new rotation (in the third plane, the plane that is parallel to the Earth's surface) is the "precession" of the wheel. TO get "maximum precession" (I assume you mean maximum angular speed inthis third plane) you would apply the maximum torque on the wheel. YOu could do this by also pulling down on the other side of the axel (opposite where the string is attached.)
So if you are sitting in a chair holding the spinning wheel, start with the wheel axel directly left-to-right (as you look at it). FOr maximum rate of transfer of angular momentum to you, you must try to apply a torque on the wheel that perfectly clockwise (or counterclockwise) from your viewpoint AND another torque that is in the plane parallel to the ground.
This second torque on the wheel is to STOP the precession of the wheel, and in doing so , the wheel exerts a counter torque on you which causes you to start spinning. The relative moments of inertia of you and wheel will determine the final rates of spin, so "maximum precession" is not very meaningful.
So if you started with the wheel situated so that the top of the wheel spins away from you, then you exerted a clockwise torque, you would also have to push with your right hand (and pull with your left) to keep the wheel axel always right-to-left in you (now rotating) perspective.
Keep in mind that you are in a system that includes the earth, and torques are exerted on the Earth as well. (You could not do this while balancing on a thin pole, for example.) Total angular momentum for you, the wheel, and the earth, stays constant.
This is all so much simpler to show with 3-D diagrams and demonstrations.