Web information is increasingly used as evidence in solving various problems, including record matching. However, acquiring web-based resources is slow and can incur other access costs. As such, solutions often acquire only a subset of the resources to achieve a balance between acquisition cost and benefit. Unfortunately, existing work has largely ignored the issue of which resources to acquire. They also fail to emphasize on the hierarchical nature of resource acquisitions, e.g., the search engine results for two queries must be obtained before their TF-IDF cosine similarity be computed. In this paper, we propose a framework for performing cost-sensitive acquisition of resources with hierarchical dependencies, and apply it to the web resource context. Our framework is versatile, and we show that a large variety of problems can be formulated using resource dependency graphs. We solve the resource acquisition problem by casting it as a combinatorial search problem. Finally, we demonstrate the effectiveness of our acquisition framework on record matching problems of different domains.