For next place prediction, machine learning methods which incorporate contextual data are frequently used. However, previous studies often do not allow deriving generalizable methodological recommendations, since they use different datasets, methods for discretizing space, scales of prediction, prediction algorithms, and context data, and therefore lack comparability. Additionally, the cold start problem for new users is an issue. In this study, we predict next places based on one trajectory dataset but with systematically varying prediction algorithms, methods for space discretization, scales of prediction (based on a novel hierarchical approach), and incorporated context data. This allows to evaluate the relative influence of these factors on the overall prediction accuracy. Moreover, in order to tackle the cold start problem prevalent in recommender and prediction systems, we test the effect of training the predictor on all users instead of each individual one. We find that the prediction accuracy shows a varying dependency on the method of space discretization and the incorporated contextual factors at different spatial scales. Moreover, our user-independent approach reaches a prediction accuracy of around 75%, and is therefore an alternative to existing user-specific models. This research provides valuable insights into the individual and combinatory effects of model parameters and algorithms on the next place prediction accuracy. The results presented in this paper can be used to determine the influence of various contextual factors and to help researchers building more accurate prediction models. It is also a starting point for future work creating a comprehensive framework to guide the building of prediction models.