In recent years, considerable endeavors have been devoted to exploring Wi-Fi-based sensing technologies by modeling the intricate mapping between received signals and corresponding human activities. However, the inherent complexity of Wi-Fi signals poses significant challenges for practical applications due to their pronounced susceptibility to deployment environments. To address this challenge, we delve into the distinctive characteristics of Wi-Fi signals and distill three pivotal factors that can be leveraged to enhance generalization capabilities of deep learning-based Wi-Fi sensing models: 1) effectively capture valuable input to mitigate the adverse impact of noisy measurements; 2) adaptively fuse complementary information from multiple Wi-Fi devices to boost the distinguishability of signal patterns associated with different activities; 3) extract generalizable features that can overcome the inconsistent representations of activities under different environmental conditions (e.g., locations, orientations). Leveraging these insights, we design a novel and unified sensing framework based on Wi-Fi signals, dubbed UniFi, and use gesture recognition as an application to demonstrate its effectiveness. UniFi achieves robust and generalizable gesture recognition in real-world scenarios by extracting discriminative and consistent features unrelated to environmental factors from pre-denoised signals collected by multiple transceivers. To achieve this, we first introduce an effective signal preprocessing approach that captures the applicable input data from noisy received signals for the deep learning model. Second, we propose a multi-view deep network based on spatio-temporal cross-view attention that integrates multi-carrier and multi-device signals to extract distinguishable information. Finally, we present the mutual information maximization as a regularizer to learn environment-invariant representations via contrastive loss without requiring access to any signals from unseen environments for practical adaptation. Extensive experiments on the Widar 3.0 dataset demonstrate that our proposed framework significantly outperforms state-of-the-art approaches in different settings (99% and 90%-98% accuracy for in-domain and cross-domain recognition without additional data collection and model training).