While the human hand is the most natural tool for interacting with objects, hand interaction with virtual objects is still a challenging research field. We recognize that common hand interaction involves two separate stages with different aspects: One is the robustness of grasping, and the other is the dexterity of manipulation after grasping a virtual object. In this paper, we address virtual hand interaction by decoupling these two aspects and propose strategic simulation algorithms for two different stages. As for the initial grasping, a quality measure-based grasping algorithm is applied for robustness, and the manipulation is simulated by physically based methods to meet the requirements of dexterity. We conducted experiments to evaluate the effectiveness of our proposed method under different display environments - monoscopic and stereoscopic. From the 2-way ANOVA test, we were able to show that the proposed scheme that separates a pre-contact grasping phase and a post-contact manipulation phase gives us the robustness of grasping quality and dexterity of tool operation. Furthermore, we demonstrate various assembly manipulations of the relatively complex models using our interaction scheme.