  This paper presents a full simulation study of the measurement of the
production cross section ($\sigma_{\mathrm{ZH}}$) of the Higgsstrahlung process
$\mathrm{e^{+}e^{-}\rightarrow ZH}$ and the Higgs boson mass ($M_{\mathrm{H}}$)
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 $\sqrt{s}$ = 250,
350, and 500 GeV, and two beam polarizations $\mathrm{e_{L}^{-}e_{R}^{+}}$ and
$\mathrm{e_{R}^{-}e_{L}^{+}}$, for which the polarizations of $\mathrm{e^{-}}$
and $\mathrm{e^{+}}$ are $\left(P\mathrm{e^{-}},P\mathrm{e^{+}}\right)$
=($-$80\%, +30\%) and (+80\%, $-$30\%), respectively. Assuming an integrated
luminosity of 250 $\mathrm{fb^{-1}}$ for each beam polarization at $\sqrt{s}$ =
250 GeV, where the best lepton momentum resolution is obtainable,
$\sigma_{\mathrm{ZH}}$ and $M_{\mathrm{H}}$ can be determined with a precision
of 2.5\% and 37 MeV for $\mathrm{e_{L}^{-}e_{R}^{+}}$ and 2.9\% and 41 MeV for
$\mathrm{e_{R}^{-}e_{L}^{+}}$, respectively. Regarding a 20 year ILC physics
program, the expected precisions for the $\mathrm{HZZ}$ coupling and
$M_{\mathrm{H}}$ are estimated to be 0.4\% and 14 MeV, respectively. The event
selection is designed to optimize the precisions of $\sigma_{\mathrm{ZH}}$ and
$M_{\mathrm{H}}$ while minimizing the bias on the measured
$\sigma_{\mathrm{ZH}}$ 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 $\sigma_{\mathrm{ZH}}$ 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 precisons and
serve as a benchmark for the planning of the ILC run scenario.
