This is the first of a series of three papers devoted to the calibration of a few parameters of crucial importance in the modeling of the evolution of intermediate-mass stars, giving special attention to the amount of convective core overshoot. To this end we acquired deep V and R photometry for three globular clusters of the Large Magellanic Cloud, namely, NGC 2173, SL 556, and NGC 2155, in the age interval 1-3 Gyr. In this first paper, we describe the aim of the project and Very Large Telescope observations and data reduction and we make preliminary comparisons of the color-magnitude diagrams with both the Padova and Yonsei-Yale isochrones. Two following papers in this series present the results of a detailed analysis of these data, independently carried out by members of the Yale and Padova stellar evolution groups. This allows us to compare both sets of models and discuss their main differences, as well as the systematic effects that they would have on the determination of the ages and metallicities of intermediate-age single-stellar populations. Based on observations collected at the European Southern Observatory, Paranal, Chile (ESO 64.L-0385).