In a series of papers, we study the stellar dynamics of the grand design barred-spiral galaxy NGC 1300. In the first paper of this series, we estimate the gravitational potential and we give it in a form suitable to be used in dynamical studies. The estimation is done directly from near-infrared observations. Since the 3D distribution of the luminous matter is unknown, we construct three different general models for the potential corresponding to three different assumptions for the geometry of the system, representing limiting cases: a pure 2D disc, a cylindrical geometry (thick disc) and a third case, where a spherical geometry is assumed to apply for the major part of the bar. For the potential of the disc component on the galactic plane, a Fourier decomposition method is used, which allows us to express it as a sum of trigonometric terms. Both even and odd components are considered, so that the estimated potential accounts also for the observed asymmetries in the morphology. For the amplitudes of the trigonometric terms, a smoothed cubic interpolation scheme is used. The total potential in each model may include two additional terms (Plummer spheres) representing a central mass concentration and a dark halo component, respectively. In all examined models, the relative force perturbation points to a strongly non-linear gravitational field, which ranges from 0.45 to 0.8 of the axisymmetric background with the pure 2D being the most non-linear one. The force perturbation in each model is found to be robust to small changes of the required parameter values. We present the topological distributions of the stable and unstable Lagrangian points as a function of the pattern speed (Ωp). The topological distribution found deviates in several cases from the classical paradigm with two stable Lagrangian points at the sides of the bar and two unstable ones close to the ends of the bar. In all three models, there is a range of Ωp values, where we find multiple stationary points whose stability affects the overall dynamics of the system.