Reliable dynamical properties from molecular dynamics simulations require careful control of thermostatting artifacts. We systematically assess how NVE, deterministic thermostats, velocity-rescale dynamics, and stochastic Langevin-type thermostats affect time-correlation functions across liquids of varying complexity. The analysis spans vibrational spectra, velocity and pressure autocorrelations, diffusion coefficients, shear viscosities, and Markov state models. Deterministic thermostats and velocity-rescale dynamics closely reproduce NVE reference data over all observables. In contrast, strongly coupled stochastic thermostats (tau less 1 ps) systematically distort dynamical properties. By constrast, moderate stochastic coupling (tau eq. 1 ps) restores near-NVE behavior while maintaining canonical sampling. Our results provide practical guidelines for selecting thermostat schemes when accurate dynamical properties or Markov models are required.