The thermodynamic changes occurring upon mixing small monovalent alcohols and water are systematically analyzed as a function of both the size and shape of the apolar group of the alcohols and of the mixture composition. For this purpose, the Helmholtz free energy, energy and entropy of mixing of the eight smallest alcohols, i.e., methanol, ethanol, propanol, isopropanol, butanol, isobutanol, s-butanol, and t-butanol with water are calculated in the entire composition range by means of Monte Carlo simulations and thermodynamic integration with three different model combinations. The obtained results are in a satisfactory agreement with existing experimental data. In particular, they are able to well reproduce the qualitative trends, being in the focus of this study. Our results indicate that the thermodynamics of mixing of these systems is primarily governed by the entropic term. In particular, the addition of alcohol to water-rich systems induces an ordering of the water molecules through hydrophobic hydration, while the addition of water to alcohol-rich mixtures induces ordering of the alcohol molecules by providing them additional H-bonds. According to the obtained free energy of mixing data, the former of these two effects clearly becomes more pronounced with increasing size and decreasing branching (i.e., increasing surface area) of the apolar groups, while the latter one is much less sensitive to the apolar tail. As a consequence, the increase of the apolar tail (and the decrease of its branching) leads to partial miscibility of the alcohols with water, with a miscibility gap occurring in water-rich compositions.