We construct an interacting lattice model for twisted ${MoTe}_2$ bilayers at a twist angle of approximately 3.7. We use the infinite density matrix renormalization group (iDMRG) in a cylinder geometry to identify a variety of competing integer and fractional Chern insulators (CIs/FCIs) and charge-density-wave (CDW) states that emerge upon the spontaneous breaking of time-reversal symmetry by valley polarization. We use finite-size analysis to establish the robustness of Chern insulating states even in geometries that admit competing CDWs, and explore the phase transitions between these states driven by increasing sublattice potential or interaction strength. Our work highlights the crucial role played by direct spin exchange in stabilizing the parent valley-polarized Chern ferromagnet band, and by mixing with higher bands in destabilizing CIs/FCIs in favor of CDW orders.