Improvement in early Alzheimer's disease (AD) diagnosis using EEG, as a consequence of advances in Machine Learning (ML) techniques, may be a valuable asset to physicians. However, in order to disseminate the use of this technology through distinct areas of the globe, from developed to developing countries, from urban to rural regions and from dense to underpopulated regions, the system must be simple, reliable and economically viable. Towards this goal, we evaluated automatic AD-EEG diagnosis accuracy changes before and after feature selection. Nineteen AD patients and 17 healthy subjects (HS) had their resting-state 32-channel EEG recorded for 25 minutes. Power spectrum density (PSD) in bands delta (1.5 - 6 Hz), theta (6.5 - 8 Hz), alpha₁ (8.5 - 10 Hz), alpha₂ (10.5 - 12 Hz), beta₁ (12.5 - 18 Hz), beta₂ (18.5 - 21 Hz) and beta₃ (21.5 - 30 Hz) were extracted from EEG signals. After that, participants were automatically classified as AD or HS with eight different machine learning algorithms under Regression, Tree, Support Vector Machine (SVM) and Ensemble categories. Lastly, feature selection (FS) yielded a robust reduction to the number of features and channels needed and also improved classification performance. After FS, the Regression, SVM and Ensemble categories displayed average accuracy of 95.6% (92.86 - 97.14), F1 score of 97.74% (96.3 - 98.55), channel numbers 25.88 (10.4 - 31) and number of features 68.52 (13.18 - 93.4). Our results suggest that reducing the number of features and channels may not only optimize the computational and equipment cost, as well as EEG test preparation time and complexity (due to the reduced number of channels), but also increase the discriminatory power of classifiers.