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 at z similar to 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 is rendered 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.