Combining data of different types and from different sources for the classification of tree species has gained popularity recently, but training models on such datasets often requires more computational demands and does not always result in higher accuracy due to feature redundancy and irrelevance. Thus preprocessing data using dimensionality reduction (DR) methods can be employed to improve the classification accuracy and reduce computations. The objective of this research is to investigate and compare tree species classification performance for different classification algorithms [naive Bayes (NB), logistic regression (LR), random forest (RF), and support vector machine (SVM)], combined with various DR methods (correlation-based feature selection filter, information gain, wrapper methods, and principal component analysis). Two primary datasets are used—QuickBird and LiDAR, as well as derived topography data. When DR is used prior to classification, the NB classifier had a significant improvement in accuracy. SVM and RF had the best classification accuracy without DR. The overall accuracies (OA) of SVM and RF are 88.2% and 87.2% (kappa 0.84 and 0.83), respectively, followed closely by LR (OA: 84.8%, kappa: 0.79) and more distantly by NB (OA: 79%, kappa: 0.72). It is recommended to use SVM and RF without DR or NB with DR for tree species classification.