This paper presents a full simulation study of the measurement of the production cross section (σZH) of the Higgsstrahlung process e+e−→ZH and the Higgs boson mass (MH) at the International Linear Collider (ILC), using events in which a Higgs boson recoils against a Z boson decaying into a pair of muons or electrons. The analysis is carried out for three center-of-mass energies s=250, 350, and 500 GeV, and two beam polarizations eL−eR+ and eR−eL+, for which the polarizations of e− and e+ are (Pe−,Pe+)=(−80%,+30%) and (+80%, −30%), respectively. Assuming an integrated luminosity of 250  fb−1 for each beam polarization at s=250  GeV, where the best lepton momentum resolution is obtainable, σZH and MH can be determined with a precision of 2.5% and 37 MeV for eL−eR+ and 2.9% and 41 MeV for eR−eL+, respectively. Regarding a 20 year ILC physics program, the expected precisions for the HZZ coupling and MH are estimated to be 0.4% and 14 MeV, respectively. The event selection is designed to optimize the precisions of σZH and MH while minimizing the bias on the measured σZH due to discrepancy in signal efficiencies among Higgs decay modes. For the first time, model independence has been demonstrated to a sub-percent level for the σZH measurement at each of the three center-of-mass energies. The results presented show the impact of center-of-mass energy and beam polarization on the evaluated precisions and serve as a benchmark for the planning of the ILC run scenario.