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We use a data-driven approach to study the magnetic and thermodynamic properties of van der Waals (vdW) layered materials. We investigate monolayers of the form$$\hbox {A}_2\hbox {B}_2\hbox {X}_6$$${\text{A}}_2{\text{B}}_2{\text{X}}_6$, based on the known material$$\hbox {Cr}_2\hbox {Ge}_2\hbox {Te}_6$$${\text{Cr}}_2{\text{Ge}}_2{\text{Te}}_6$, using density functional theory (DFT) calculations and machine learning methods to determine their magnetic properties, such as magnetic order and magnetic moment. We also examine formation energies and use them as a proxy for chemical stability. We show that machine learning tools, combined with DFT calculations, can provide a computationally efficient means to predict properties of such two-dimensional (2D) magnetic materials. Our data analytics approach provides insights into the microscopic origins of magnetic ordering in these systems. For instance, we find that the X site strongly affects the magnetic coupling between neighboring A sites, which drives the magnetic ordering. Our approach opens new ways for rapid discovery of chemically stable vdW materials that exhibit magnetic behavior.