  Ruddlesden-Popper (RP) phases of
Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) are evolved
as new promising class of chalcogenide perovskites in the field of
optoelectronics, especially in solar cells. However, detailed studies regarding
its optical, excitonic, polaronic and transport properties are hitherto
unknown. Here, we have explored the excitonic and polaronic effect in RP phases
of Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) using
several first-principles based state-of-the-art methodologies under the
framework of Many Body Perturbation Theory. Unlike it's bulk counterpart, the
optical and excitonic anisotropy are observed in
Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]) RP phases.
From Wannier-Mott approach, we show that in the RP phases of this class of
chalcogenide perovskites, capturing the ionic contribution to the dielectric
constant is important. We report significant ionic contribution and relatively
smaller electron-phonon coupling constant for
Ba$_{\textrm{n+1}}$Zr$_\textrm{n}$S$_{\textrm{3n+1}}$ in comparison to the bulk
BaZrS$_3$. The exciton binding energy is found to be dependent on the presence
of large electron-phonon coupling. The charge carrier mobility is maximum in
Ba$_2$ZrS$_4$, computed employing deformation potential of the same. As per our
analysis, the optical phonon modes are observed to dominate the acoustic phonon
modes, leading to decrease in polaron mobility on increasing n in
Ba$_{\textrm{n+1}}$Zr$_{\textrm{n}}$S$_{\textrm{3n+1}}$ (n=[1-3]).
