A major concern in cloud/edge storage systems is serving a large number of users simultaneously. The service rate region is introduced recently as an important performance metric for coded distributed systems, which is defined as the set of all data access requests that can be simultaneously handled by the system. This paper studies the problem of designing a coded distributed storage system storing k files where a desired service rate region R of the system is given and the goal is 1) to determine the minimum number of storage nodes n(R) (or a lower bound on n(R)) for serving all demand vectors inside the set R and 2) to design the most storage-efficient redundancy scheme with the service rate region covering R. Towards this goal, we propose three general lower bounds for n(R). Also, for k=2, we characterize n(R), i.e., we show that the proposed lower bounds are tight via designing a novel storage-efficient redundancy scheme with n(R) storage nodes and the service rate region covering R.