We propose a novel Memristive-Friendly Echo State Network (MF-ESN) architecture, named MF-RingESN, that leverages structured connectivity patterns derived from minimum complexity principles. Specifically, the proposed model adopts the Simple Cycle Reservoir (SCR) topology within a memristive-friendly computational framework. We evaluate our approach on a diverse suite of time series classification and regression tasks. Our results demonstrate that the MF-RingESN maintains or improves upon the performance of the original MF-ESN while significantly reducing the complexity of the reservoir structure, thereby enabling more efficient and potentially more sustainable neuromorphic computing implementations.