  The advent of the James Webb Space Telescope (JWST) signals a new era in
exploring galaxies in the high-$z$ universe. Current and upcoming JWST imaging
will potentially detect galaxies out to $z \sim 20$, creating a new urgency in
the quest to infer accurate photometric redshifts (photo-$z$) for individual
galaxies from their spectral energy distributions, as well as masses, ages and
star formation rates. Here we illustrate the utility of informed priors
encoding previous observations of galaxies across cosmic time in achieving
these goals. We construct three joint priors encoding empirical constraints of
redshifts, masses, and star formation histories in the galaxy population within
the \prospector\ Bayesian inference framework. In contrast with uniform priors,
our model breaks an age-mass-redshift degeneracy, and thus reduces the mean
bias error in masses from 0.3 to 0.1 dex, and in ages from 0.6 to 0.2 dex in
tests done on mock JWST observations. Notably, our model recovers redshifts at
least as accurately as the state-of-the-art photo-$z$ code \eazy\ in deep JWST
fields, but with two advantages: tailoring a model based on a particular survey
renders mostly unnecessary given well-motivated priors; obtaining joint
posteriors describing stellar, active galactic nuclei, gas, and dust
contributions becomes possible. We can now confidently use the joint
distribution to propagate full non-Gaussian redshift uncertainties into
inferred properties of the galaxy population. This model,
``\prospector-$\beta$'', is intended for fitting galaxy photometry where the
redshift is unknown, and will be instrumental in ensuring the maximum science
return from forthcoming photometric surveys with JWST. The code is made
publicly available online as a part of \prospector.
