Hey.
Well, the chassis will probably need to be built around the engine, fuel/battery supply and the servos used to control the steering, and the throttle. If the engine is electric (motor), then the motor doesn't need a servo, but some sort of speed controll. Material to use should be stiff, yet flexible enough to take the shock and vibration. Plastic, wood, or sheet metal are ok materials to use. Wood and rigid plastics, epoxy based, are probably not flexible enough to hold up. Some RC car chassis are built with epoxy-resin fiberglass molds, or from some sort of composite material like carbon fiber.
Typically, the engine is mounted on the rear of the chassis. Most engines are mounted leading the rear axle, perpendicular to the axle. I suppose the mounting depends on the gear box as well.
Most RC car wheels are attached to the chassis on a spindle. The wheel is held on by a locknut. The wheel contains a bearing or bushing, which glides on the spindle.
I suppose looking at some of the already designed RC cars will help you understand better than I could explain. Check out some of the designs on the Web, or go to a hobby store and look at the chassis or a RC car.
Your largest challenges will be motor mounting, transmission and rear axle organization. Then comes suspension and power, radio gear. Then, should come chassis.