Online planner selection is the task of choosing a solver out of a predefined set for a given planning problem. As planning is computationally hard, the performance of solvers varies greatly on planning problems. Thus, the ability to predict their performance on a given problem is of great importance. While a variety of learning methods have been employed, for classical cost-optimal planning the prevailing approach uses Graph Neural Networks (GNNs). In this work, we continue the line of work on using GNNs for online planner selection. We perform a thorough investigation of the impact of the chosen GNN model, graph representation and node features, as well as prediction task. Going further, we propose using the graph representation obtained by a GNN as an input to the Extreme Gradient Boosting (XGBoost) model, resulting in a more resource-efficient yet accurate approach. We show the effectiveness of a variety of GNN-based online planner selection methods, opening up new exciting avenues for research on online planner selection.