Tin selenide is a layered material that captured the interest of the scientific community for its stunning thermoelectric properties and fascinating phase transitions under pressure. Recently, an experimental study revealed the existence of a topological and superconducting phase in its pressure-stabilized CsCl-type phase. By means of ab initio techniques, we investigate the structural properties of this compound and its pressure phase diagram, comparing our findings with the experimental results. We then focused on the electronic features of the topological CsCl-type phase and analyze its dynamical and superconducting properties. To understand the origin of the superconducting transition, we predict the critical temperature as a function of the pressure, T_c(P), by the superconducting density-functional theory and analyze the behavior of the resistance with pressure and temperature by means of a percolative model. The careful comparison of calculations with available experiments reveals that inhomogeneities and nonhydrostatic pressure effects are relevant in this system.