The paper explores spread and spectral complexity in quantum spin chains transitioning from integrable to chaotic behavior, focusing on the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ model. It confirms that a peak in spread complexity before saturation is a characteristic feature of chaotic systems. The saturation value of spread complexity depends on the Hamiltonian's spectral statistics and the specific state, but a universal bound is determined by the system's symmetries and dimensions, realized by the thermofield double (TFD) state at infinite temperature. The time scales of spread complexity and spectral form factor (SFF) agree and are independent of chaotic properties. For spectral complexity, the saturation value and timescale are determined by the minimum energy difference in the spectrum, explaining earlier saturation in chaotic systems compared to integrable ones. The TFD state is conjectured to be suitable for probing chaos in quantum many-body systems. The study shows that spread and spectral complexity exhibit distinct features in chaotic systems, with spread complexity showing a peak and spectral complexity saturating, both governed by the minimum energy difference. These results align with studies on Krylov operator complexity, and the saturation timescales are proportional to the inverse of the minimum energy difference. The paper concludes that these complexities provide insights into quantum chaos in many-body systems.The paper explores spread and spectral complexity in quantum spin chains transitioning from integrable to chaotic behavior, focusing on the mixed-field Ising model and the next-to-nearest-neighbor deformation of the Heisenberg XXZ model. It confirms that a peak in spread complexity before saturation is a characteristic feature of chaotic systems. The saturation value of spread complexity depends on the Hamiltonian's spectral statistics and the specific state, but a universal bound is determined by the system's symmetries and dimensions, realized by the thermofield double (TFD) state at infinite temperature. The time scales of spread complexity and spectral form factor (SFF) agree and are independent of chaotic properties. For spectral complexity, the saturation value and timescale are determined by the minimum energy difference in the spectrum, explaining earlier saturation in chaotic systems compared to integrable ones. The TFD state is conjectured to be suitable for probing chaos in quantum many-body systems. The study shows that spread and spectral complexity exhibit distinct features in chaotic systems, with spread complexity showing a peak and spectral complexity saturating, both governed by the minimum energy difference. These results align with studies on Krylov operator complexity, and the saturation timescales are proportional to the inverse of the minimum energy difference. The paper concludes that these complexities provide insights into quantum chaos in many-body systems.