This paper addresses the multi-faceted problem of robot grasping, where multiple criteria may conflict and differ in importance. We introduce a probabilistic framework, Grasp Ranking and Criteria Evaluation (GRaCE), which employs hierarchical rule-based logic and a rank-preserving utility function for grasps based on various criteria such as stability, kinematic constraints, and goal-oriented functionalities. GRaCE's probabilistic nature means the framework handles uncertainty in a principled manner, i.e., the method is able to leverage the probability that a given criteria is satisfied. Additionally, we propose GRaCE-OPT, a hybrid optimization strategy that combines gradient-based and gradient-free methods to effectively navigate the complex, non-convex utility function. Experimental results in both simulated and real-world scenarios show that GRaCE requires fewer samples to achieve comparable or superior performance relative to existing methods. The modular architecture of GRaCE allows for easy customization and adaptation to specific application needs.