  The past decade has seen impressive progress in the detection of $z>7$
galaxies with the Hubble Space Telescope, however little is known about their
properties. The James Webb Space Telescope will revolutionise the high-$z$
field by providing NIR (i.e., rest-frame optical) data of unprecedented depth
and spatial resolution. Measuring galaxy quantities such as resolved stellar
ages or gas metallicity gradients traditionally requires spectroscopy, as
broad-band imaging filters are generally too coarse to fully isolate
diagnostics such as the 4000 \r{A} (rest-frame) break, continuum emission from
aged stars, and key emission lines (e.g., [OII], [OIII], H$\beta$). However, in
this paper, we show that adding NIRCam images through a strategically chosen
medium-band filter to common wide-band filters sets adopted by ERS and GTO
programs delivers tighter constraints on these galactic properties. To
constrain the choice of filter, we perform a systematic investigation of which
combinations of wide-band filters from ERS and GTO programs and single
medium-band filters offer the tightest constraints on several galaxy properties
at redshifts $z\sim7-11$. We employ the JAGUAR extragalactic catalogs to
construct statistical samples of physically-motivated mock photometry and
conduct SED-fitting procedures to evaluate the accuracy of galaxy property (and
photo-$z$) recovery with a simple star-formation history model. We find that
adding $>4.1 \mu$m medium filters at comparable depth to the broad-band filters
can significantly improve photo-$z$s and yield close to order-of-magnitude
improvements in the determination of quantities such as stellar ages,
metallicities, SF-related quantities and emission line fluxes at $z\sim8$. For
resolved sources, the proposed approach enables spatially-resolved
determination of these quantities that would be prohibitive with slit
spectroscopy.
