Vibration is caused by some unbalance like bad tyres, worn engine mounts or things like that.

Play in the suspension or steering may make it worse but will not cause it. Excessive play lead to loose steering, wandering of the car, reaction to road conditions (more shaking than vibration). Bad steering shock leads to shaking of the car when crossing to transversal road disturbances, link repairs of the road and crossing railroad tracks, not vibration.

You can feel vibration of the wheels in the steering wheel, vibrations of the engine or transmission are more general and not more noticeable in the steering wheel.
What tyres do you have, some (all cheap) tyres are not suited for a Mercedes, these cars are very sensitive.

Before you start taking the suspension apart I would advise you to find the cause.

If you feel the vibration in the steering wheel start with testing (borrowing) a set of wheel that are tested with an other car.

If the vibration is not primarily in the steering wheel check engine/transmission mounts and drive shaft. Even if the vibration is only when driving it may still be bad mounts, under load the mounts are much more stressed than standing still.