Integrated sensing and communication (ISAC) has emerged as a transformative paradigm, enabling situationally aware and perceptive next-generation wireless networks through the co-design of shared network resources. With the adoption of millimeter-wave (mmWave) and terahertz (THz) frequency bands, ultra-massive MIMO (UM-MIMO) systems and holographic surfaces unlock the potential of near-field (NF) propagation, characterized by spherical wavefronts that facilitate beam manipulation in both angular and range domains. This paper presents a unified approach to near-field beam-training and sensing, introducing a dual-purpose codebook design that employs discrete Fourier transform (DFT)-based codebooks for coarse estimation of sensing parameters and polar codebooks for parameter refinement. Leveraging these range and angle estimates, a customized low-complexity space-time adaptive processing (STAP) technique is proposed for NF-ISAC to detect slow-moving targets and efficiently mitigate clutter. The interplay between codebooks and NF-STAP framework offers three key advantages: reduced communication beam training overhead, improved estimation accuracy, and minimal STAP computational complexity. Simulation results show that the proposed framework can reduce STAP complexity by three orders of magnitude, validating efficacy, and highlighting the potential of the proposed approach to seamlessly integrate NF communication and sensing functionalities in future wireless networks.