  A primary goal of a future $e^+e^-$ collider program will be the precision
measurement of Higgs boson properties. For practical reasons it is of interest
to determine the minimal set of detector specifications required to reach this
and other scientific goals. Such information could be useful in developing a
staged approach to the full collider project with an initial lower-cost version
focused on achieving some of the primary scientific objectives. Here we
investigate the precision obtainable for the $e^+ e^- \rightarrow Z h
\rightarrow \mu^+ \mu^- X$ inclusive cross section and the Higgs boson mass
using the di-muon recoil method, considering a detector that has only an inner
tracking system within a solenoidal magnetic field, surrounded by many nuclear
interaction lengths of absorbing material, and an outer muon identification
system. We find that the sensitivity achievable in these measurements with such
a tracking detector is only marginally reduced compared to that expected for a
general purpose detector with additional electromagnetic and hadronic
calorimeter systems. The difference results mainly from multi-photon
backgrounds that are not as easily rejected with tracking detectors. We also
comment on the prospects for an analogous measurement of the inclusive cross
section $\sigma( e^+ e^- \to Z h \to e^+ e^- X)$. Finally, we study searches
for light scalars utilizing the di-muon recoil method, estimating the projected
reach with a tracking and general purpose detector.
