Diabetic foot ulcers (DFUs) are a severe complication of diabetes mellitus, associated with high rates of amputation and mortality. Automated detection and segmentation from clinical images could support timely intervention and remote monitoring, yet existing approaches lack systematic benchmarks and rarely exploit the synergy between lesion localization and delineation. In this work, we present a comprehensive and insight-driven study of detection and segmentation strategies for DFU analysis using datasets from the Diabetic Foot Ulcer Challenge (DFUC). We benchmark four state-of-the-art object detection frameworks alongside an in-depth optimization study, and evaluate four global segmentation models. Furthermore, we propose a hybrid detection-guided segmentation pipeline leveraging a domain-adapted foundation model. Our analysis reveals that, in detection-guided pipelines, lesion coverage (recall) is more critical than standard detection metrics such as mAP, and that the quality of spatial prompts plays a key role in downstream segmentation performance. Ensemble strategies are further explored to improve robustness and generalization. The optimized detection ensemble ranks first on the DFUC2020 challenge leaderboard, and the proposed segmentation pipeline achieves Dice scores of up to 0.721 and 0.786 on two independent test sets with distinct acquisition conditions, demonstrating consistent generalization beyond the training distribution. These results provide design guidelines and a comprehensive benchmark for automated DFU analysis.