This work investigates the hydrodynamic performance of various configurations of concrete floating modules and mooring systems, which are suited for a shallow water marine environment with a depth of 60 m. A comparative analysis of the hydrodynamic shapes of floating modules was conducted, including modules combining flat plate and semi-submersible design, semi-submersible modules, and column-type modules. This work also compared the catenary chain’s performance, including catenary chains and catenary chains complemented with segmented weight clumps. The paper underlines the functional characteristics of floating modules, the performance of distinct hydrodynamic shapes, and both the economic indicators and restoring force of the mooring systems. Findings suggest that flat plates with circular truncated cone modules aptly fulfill the hydrodynamic performance requirements and can provide superior load-bearing efficiency. Furthermore, using catenary chains with segmented weight clumps can improve the motion response performance of the platforms, under the same mooring chain length and safety requirements, thereby bringing greater economic benefits. This work can potentially aid in the investigation of the hydrodynamic performance and design of mooring systems for modular floating structures.