We study the high-Tc cuprate HgBa2CuO4+? by solving an ab initio low-energy effective Hamiltonian with many-variable variational Monte Carlo method. To determine the ground state, we utilized the single Lanczos step and/or combined a fat-tree tensor network to perform the variance extrapolation of energies. In the underdoped region, we found that a charge ordered state with periodicity of 4 unit cells competes with homogeneous states, which is consistent with the observations by recent X-ray scattering experiments. We also clarify the strong impact of off-site interactions on the superconductivity as well as the tight connection among superconductivity, inhomogeneity, and the Mottness.