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The angulon, a quasiparticle formed by a quantum rotor dressed by the excitations of a many-body bath, can be used to describe an impurity rotating in a fluid or solid environment. Here we propose a coherent state ansatz in the co-rotating frame which provides a comprehensive theoretical description of angulons. We reveal the quasiparticle properties, such as energies, quasiparticle weights and spectral functions, and show that our ansatz yields a persistent decrease in the impurity's rotational constant due to many-body dressing, consistent with experimental observations. From our study, a picture of the angulon emerges as an effective spin interacting with a magnetic field that is self-consistently generated by the molecule's rotation. Moreover, we discuss rotational spectroscopy, which focuses on the response of rotating molecules to a laser perturbation in the linear response regime. Importantly, we take into account initial-state interactions that have been neglected in prior studies and reveal their impact on the excitation spectrum. To examine the angulon instability regime, we use a single-excitation ansatz and obtain results consistent with experiments, in which a broadening of spectral lines is observed while phonon wings remain highly suppressed due to initial-state interactions.