This work proposes a novel framework to dynamically and effectively manage and allocate different types of resources for Metaverse applications, which are forecasted to demand massive resources of various types that have never been seen before. Specifically, by studying functions of Metaverse applications, we first propose an effective solution to divide applications into groups, namely MetaInstances, where common functions can be shared among applications to enhance resource usage efficiency. Then, to capture the real-time, dynamic, and uncertain characteristics of request arrival and application departure processes, we develop a semi-Markov decision process-based framework and propose an intelligent algorithm that can gradually learn the optimal admission policy to maximize the revenue and resource usage efficiency for the Metaverse service provider and at the same time enhance the Quality-of-Service for Metaverse users. Extensive simulation results show that our proposed approach can achieve up to 120% greater revenue for the Metaverse service providers and up to 178.9% higher acceptance probability for Metaverse application requests than those of other baselines.