The shape of the dark matter halo of a galaxy offers valuable clues on the physical nature of dark matter. In this series of papers, we model the structure and kinematics of the baryons in edge-on galaxies. The flaring of the H I disk provides a measure of the vertical force field of that disk. In a similar way, the rotation curve provides a measure of the horizontal force field. As the galaxies are at rest, the combination of these two provides all the required ingredients for full hydrostatic models. We use these models to analyze their potential wells as generated by the dark matter halo and its shape. In this first paper, we explain this project in more detail and present the H I observations of our sample of 8 edge-on galaxies. We also...