This paper addresses the stabilization problem of stochastic jump systems (SJSs) closed by a generally sampled controller. Because of the controller's switching and state both sampled, it is challenging to study its stabilization. A new stabilizing method deeply depending on the mode classifications is proposed to deal with the above sampling situation, whose quantity is equal to a Stirling number of the second kind. For the sake of finding the best stabilization effect among all the classifications, a convex optimization problem is developed, whose globally solution is proved to be existent and can be computed by an augmented Lagrangian function. More importantly, in order to further reduce the computation complexity but retaining a better performance as much as possible, a novelly improved hill-climbing algorithm is established by applying the Q-learning technique to provide an optimal attenuation coefficient. A numerical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study.