Document stores have become one of the key NoSQL storage solutions. They have been widely adopted in different domains due to their ability to store semi-structured data and expressive query capabilities. However, implementations differ in terms of concrete data storage and retrieval. Unfortunately, a standard framework for data and query optimization for document stores is nonexistent, and only implementation-specific design and query guidelines are used. Hence, the goal of this work is to aid automating the data design for document stores based on query costs instead of generic design rules. For this, we define a generic storage and query cost model based on disk access and memory allocation that allows estimating the impact of design decisions. Since all document stores carry out data operations in memory, we first estimate the memory usage by considering characteristics of the stored documents, their access patterns, and memory management algorithms. Then, using this estimation and metadata storage size, we introduce a cost model for random access queries. We validate our work on two well-known document store implementations: MongoDB and Couchbase. The results show that the memory usage estimates have the average precision of 91% and predicted costs are highly correlated to the actual execution times. During this work, we have managed to suggest several improvements to document storage systems. Thus, this cost model also contributes to identifying discordance between document store implementations and their theoretical expectations.