In learning-based control, model predictive control (MPC) is frequently employed due to the broad usability of various data-based models for predicting system dynamics. The uncertainty inherent in these models, influenced by factors such as training data or method, is typically treated as unknown. In this work, Gaussian Processes (GPs) are chosen as data-based models, because GPs have the advantage of quantifying the uncertainty of their predictions. In MPC, the quality of the prediction model has a significant impact on the resulting control performance. In the following, the correlation between prediction quality of the model and the control performance is investigated. Systematic exploration of various parameters affecting training is conducted. The following parameters are varied: different training datasets, different methods of rescaling the training data, different methods for constructing the reduced training subset, varying the number of training points in the subset, and employing two different methods for GP training (i.e., hyperparameter optimization). Using these methods, a GP is trained and utilized in an MPC to control a dynamic system. A simulated crane pendulum is used as a test system. The prediction and control performance is evaluated using criteria for error and input energy.