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Two-dimensional topological materials (TMs) have a variety of properties that make them attractive for applications including spintronics and quantum computation. However, there are only a few such experimentally known materials. To help discover new 2D TMs, we develop a unified and computationally inexpensive approach to identify magnetic and non-magnetic 2D TMs, including gapped and semi-metallic topological classifications, in a high-throughput way using density functional theory-based spin-orbit spillage, Wannier-interpolation, and related techniques. We first compute the spin-orbit spillage for the ~1000 2D materials in the JARVIS-DFT dataset (https://www.ctcms.nist.gov/~knc6/JVASP.html ), resulting in 122 materials with high-spillage values. Then, we use Wannier-interpolation to carry-out Z2, Chern-number, anomalous Hall conductivity, Curie temperature, and edge state calculations to further support the predictions. We identify various topologically non-trivial classes such as quantum spin-hall insulators (QSHI), quantum anomalous-hall insulators (QAHI), and semimetals. For a few predicted materials, we run G0W0+SOC and DFT+U calculations. We find that as we introduce many-body effects, only a few materials retain non-trivial band-topology, suggesting the importance of high-level DFT methods in predicting 2D topological materials. However, as an initial step, the automated spillage screening and Wannier-approach provide useful predictions for finding new topological materials and to narrow down candidates for experimental synthesis and characterization.