The dataset contains all raw data used in the publication M. Marchesini et al. “All-fiber, near-infrared, laser system at 780~nm for atom cooling”, submitted yet unpublished, together with Julia scripts implementing the fits and generating the plots of the figures. This dataset is part of the Horizon 2020 CRYST^3 project. The publication aims at disseminating a new laser system for Rb-based quantum technologies. Its peculiarity is that it is a more compact and cheaper setup respect to commercial ones, due to the use of telecom-grade components. Other than the description of the setup, the publication presents its characterization, through the data reported here. The results are compatible with the expectations of having similar characteristics of commercial systems.