Random Forests (RF) of tree classifiers are a popular ensemble method for classification. RF have shown to be effective in many different real world classification problems and nowadays are considered as one of the best learning algorithms in this context. In this paper we discuss the effect of the hyperparameters of the RF over the accuracy of the final model, with particular reference to different theoretically grounded weighing strategies of the tree in the forest. In this way we go against the common misconception which considers RF as an hyperparameter-free learning algorithm. Results on a series of benchmark datasets show that performing an accurate Model Selection procedure can greatly improve the accuracy of the final RF classifier.