Servo motor for throwing a rubber ball

It is not at all easy to answer that question.

First, you need to calculate the force necessary to accelerate the ball and the apparatus that is holding it to the necessary release speed. Then you need to find a servo that can comfortably produce that force and speed.

I cannot tell from your description if any of the servos will be part of the mass being accelerated. A diagram would make that clear.

...R