We report an investigation of the ground-state properties of americium dioxide and its sesquioxides using first-principles calculations. In order to take into account strong 5$f$ electronic correlations, we apply the generalized gradient approximation (GGA)+$U$ as well as the hybrid functionals to these compounds. We present a systematic study of several bulk properties such as structural, elastic, energetic, electronic, and magnetic properties as a function of the effective Coulomb $U$ and exchange $J$ GGA+$U$ parameters in the range of 0.0-8.0 and 0.00-0.75 eV, respectively. The values ($U, J$) = (6.00 eV, 0.75 eV) are those providing a correct description of bulk properties by comparison to the available experimental data. We discuss the effect of loss of symmetry caused by DFT+$U$ on several properties. We also discuss the effect of the spin-orbit coupling on these properties. Furthermore, we highlight that in order to reach the ground state of americium dioxide and sesquioxides using GGA+$U$ the monitoring of the occupation matrices of 5$f$ correlated orbitals is crucial. Our computational scheme provides reliable and accurate results concerning several bulk properties that have not been studied experimentally yet. For instance, our elastic constants calculated for AmO$_ 2$ follow the same trend as those of other actinide oxides (UO$_2$ , NpO$_2$ , and PuO$_2$) and can be used as reference. We have also computed the electronic and static dielectric constants, as well as the Am and O Born effective charge of americium dioxide. Finally, we find the A-type hexagonal structure to be the most stable structure at low temperature for americium sesquioxides. For this phase, we predict the internal structural parameters as well as the bulk modulus. We provide data concerning the formation enthalpy of the Am$_2$ O$_3$ bcc cubic structure.