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Network Function Virtualization (NFV) is a system that provides application services by connecting virtual network functions (VNFs), and is expected to accommodate new service requests through the development of new VNF and connection with existing ones. Because VNFs are implemented by software, their design and placement are important problems for the NFV system, which reduce the current and future system costs. In this paper, we investigate the design principles and the placement policies that reduce the cost of designing and developing VNFs for accommodating new service requests. As for the design policy, we introduce a Core/Periphery-Based Design (CPBD) that utilizes the core/periphery concept for developing VNFs. In CPBD, "core" VNFs are developed in advance and repeatedly used to accommodate future service requests. While "core" VNFs are common to current and future service requests, "periphery" VNFs are developed and customized for each service request. Next, we investigate the placement policies of VNFs for CPBD to fully utilize the nature of their core/periphery structure. In addition, we examine the Center-Located Core/Periphery placement (CLCP) policy and the Geographically-Distributed Core/Periphery placement (GDCP) policy, and evaluate the long-term cost of the NFV system under resource restrictions to run VNFs. Our results show that CPBD reduces the long-term cost of design and development of VNFs by 23% compared to the design with no core VNFs. Moreover, in the case of no resource restrictions, both CLCP and GDCP reduce the long-term costs of placing and connecting VNFs by 15% compared to the existing VNF placement algorithm. With resource constraints, GDCP reduces the long-term costs over CLCP by 11%.