The efficient deployment of fifth generation and beyond networks relies upon the seamless combination of recently introduced transmission techniques. Furthermore, as multiple network nodes exist in dense wireless topologies, low-complexity implementation should be promoted. In this work, several wireless communication techniques are considered for improving the sum-rate performance of cooperative relaying non-orthogonal multiple access (NOMA) networks. For this purpose, an opportunistic relay selection algorithm is developed, employing single-antenna relays to achieve full-duplex operation by adopting the successive relaying technique. In addition, as relays are equipped with buffers, flexible half-duplex transmission can be performed when packets reside in the buffers. The proposed buffer-aided and successive single-antenna (BASSA-NOMA) algorithm is presented in detail and its operation and practical implementation aspects are thoroughly analyzed. Comparisons with other relevant algorithms illustrate significant performance gains when BASSA-NOMA is employed without incurring high implementation complexity.