Federated Learning (FL) enables collaborative learning without exposing clients' data. While clients only share model updates with the aggregator, studies reveal that aggregators can infer sensitive information from these updates. Secure Aggregation (SA) protects individual updates during transmission; however, recent work demonstrates a critical vulnerability where adversarial aggregators manipulate client selection to bypass SA protections, constituting a Biased Selection Attack (BSA). Although verifiable random selection prevents BSA, it precludes informed client selection essential for FL performance. We propose Adversarial Robust Federated Learning (AdRo-FL), which simultaneously enables: informed client selection based on client utility, and robust defense against BSA maintaining privacy-preserving aggregation. AdRo-FL implements two client selection frameworks tailored for distinct settings. The first framework assumes clients are grouped into clusters based on mutual trust, such as different branches of an organization. The second framework handles distributed clients where no trust relationships exist between them. For the cluster-oriented setting, we propose a novel defense against BSA by (1) enforcing a minimum client selection quota from each cluster, supervised by a cluster-head in every round, and (2) introducing a client utility function to prioritize efficient clients. For the distributed setting, we design a two-phase selection protocol: first, the aggregator selects the top clients based on our utility-driven ranking; then, a verifiable random function (VRF) ensures a BSA-resistant final selection. AdRo-FL also applies quantization to reduce communication overhead and sets strict transmission deadlines to improve energy efficiency. AdRo-FL achieves up to $1.85\times$ faster time-to-accuracy and up to $1.06\times$ higher final accuracy compared to insecure baselines.