Three dimensional materials with strong spin-orbit coupling and magnetic interactions represent an opportunity to realize a variety of rare and potentially useful topological phases. In this work, we use first principles calculations to show that the recently synthesized material Bi₂MnSe₄ displays a combination of band inversion and magnetic interactions, leading to several topological phases. In bulk form, the ferromagnetic phase of Bi₂MnSe₄ is either a nodal line or Weyl semimetal, depending on the direction of the spins. When the spins are arranged in a layered antiferromagnetic configuration, the combination of time reversal plus a partial translation is a new symmetry, and the material instead becomes an antiferromagnetic topological insulator. However, the intrinsic TRS breaking at the surface of Bi₂MnSe₄ removes the typical Dirac cone feature, allowing the observation of the half-integer quantum anomalous Hall effect (AHC). Furthermore, we show that in thin film form, for some thicknesses, Bi₂MnSe₄ becomes a Chern insulator with a band gap of up to 58 meV. This combination of properties in a stoichiometric magnetic material makes Bi₂MnSe₄ an excellent candidate for displaying robust topological behavior.