A key issue in layered materials is the dependence of their properties on their chemical composition and crystal structure in addition to the dimensionality. For instance, atomically thin magnetic structures exhibit novel spin properties that do not exist in the bulk. We use first-principles calculations, based on density functional theory, and machine learning to study the magnetocrystalline anisotropy of a set of single-layer two-dimensional structures that are derived from changing the chemical composition of the ferromagnetic semiconductor Cr2Ge2Te6. We discuss trends and identify descriptors for the magnetocrystalline anisotropy in monolayers with the chemical formula A2B2X6. Our data-driven study aims to provide physical insights into the microscopic origins of magnetic anisotropy in two dimensions. For instance, we demonstrate that hybridization plays a key role in determining the magnetic anisotropy of the materials investigated in this study. In addition, we demonstrate that first-principles calculations can be combined with machine learning to create a high-throughput computational approach for the targeted design of quantum materials with potential applications in areas ranging from sensing to data storage.