Wi-Fi sensing is an innovative technology that enables numerous human-related applications. Among these, Wi-Fi based person re-identification (Re-ID) is an emerging research topic aiming to address well-known challenges related to traditional vision-based methods, such as occlusions or illumination changes. This approach can serve as either an alternative or a supplementary solution to those conventional techniques. However, public datasets and benchmarks for Wi-Fi based person Re-ID are still missing, posing constraints on future investigations. Towards filling this gap, this paper presents Wi-PER81, a pioneering dataset comprising measurements of 162,000 wireless packets captured at two different times, associated with 81 distinct identities. Furthermore, it introduces a baseline Siamese neural network architecture used to analyze person-related signal magnitude heatmaps and the results of a comparative study against well-known neural network models, serving as backbones in the proposed approach, that provides a comprehensive benchmark for person Re-ID using radio-based visual features.