  Improvements in current instruments and the advent of next-generation
instruments will soon push observational 21 cm cosmology into a new era, with
high significance measurements of both the power spectrum and the mean
("global") signal of the 21 cm brightness temperature. In this paper we use the
recently commenced Hydrogen Epoch of Reionization Array as a worked example to
provide forecasts on astrophysical and cosmological parameter constraints. In
doing so we improve upon previous forecasts in a number of ways. First, we
provide updated forecasts using the latest best-fit cosmological parameters
from the Planck satellite, exploring the impact of different Planck datasets on
21 cm experiments. We also show that despite the exquisite constraints that
other probes have placed on cosmological parameters, the remaining
uncertainties are still large enough to have a non-negligible impact on
upcoming 21 cm data analyses. While this complicates high-precision constraints
on reionization models, it provides an avenue for 21 cm reionization
measurements to constrain cosmology. We additionally forecast HERA's ability to
measure the ionization history using a combination of power spectrum
measurements and semi-analytic simulations. Finally, we consider ways in which
21 cm global signal and power spectrum measurements can be combined, and
propose a method by which power spectrum results can be used to train a compact
parameterization of the global signal. This parameterization reduces the number
of parameters needed to describe the global signal, increasing the likelihood
of a high significance measurement.
