The emerging negative capacitance FinFET (NC-FinFET) device is a promising technology for the design of low-power VLSI circuits. This paper proposes ultra-low-power, high-performance, and low-area dynamic random access memory and sequential logic circuits based on NC-FinFETs. These circuits leverage the fact that NC-FinFETs have low leakage currents which help to facilitate a dynamic storage (DS)-based logic design style. This can in turn lead to reduced area overhead and help to compensate for higher delays that may be associated with NC-FinFETs. Our proposed circuit-level solutions can improve the data retention time of DS latch, flip-flop, and eDRAM circuits. Simulations with 14nm baseline FinFET (BS-FinFET) and NC-FinFET device models reveal that the proposed circuits offer up to 83.5% improvement in area-power-delay-product when compared to conventional BS-FinFET static-storage counterparts.