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Vehicular delay-tolerant networks follow a store–carry–forward mechanism to overcome the state of broken links between source and destination, which is crucial for autonomous vehicle networks. These networks depend upon the mobility of vehicular-relay nodes, which can adopt the store–carry–forward arrangement and provide consent to utilize their resources for packet forwarding. In reality, vehicular-relay nodes drop packets because of a lack of resources and selfish behavior, leading to potential failures in networks. The reason for this failure in performance is the absence of an efficient relay node selection strategy. Typically, vehicular delay networks can provide communication solutions in challenging conditions when other traditional networks fail to perform due to disconnection. However, if the routing strategy does not consider nodes' selfish nature and relay nodes' inefficiency, packet drops continue, and the approach will fail to perform. This paper proposes a routing strategy, known as the best-choice vehicular-relay selection strategy for vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) transmission, to overcome this breakdown situation. The proposed strategy selects the best-performing vehicular-relay nodes and restricts the packet replication to low-performing vehicular nodes. The proposed routing strategy selects the best-choice relay nodes based on their past performance. Numerical analysis and our simulation results show that the proposed approach outperforms some of the leading routing strategies in its class by increasing the delivery probability, decreasing the overhead ratio, average latency, and the number of dropped packets in the vehicular network. [ABSTRACT FROM AUTHOR]