  [Abridged] It is widely accepted that observations at mid-infrared (mid-IR)
wavelengths enable the selection of galaxies with nuclear activity, which may
not be revealed even in the deepest X-ray surveys. In this work new near- and
mid-IR color diagnostics are explored, aiming for improved efficiency - better
completeness and less contamination - in selecting AGN out to very high
redshifts. We restrict our study to the James Webb Space Telescope wavelength
range (0.6-27um). The criteria are created based on the predictions by
state-of-the-art galaxy and AGN templates covering a wide variety of galaxy
properties, and tested against control samples with deep multi-wavelength
coverage (ranging from the X-rays to radio frequencies). We show that the
colors Ks-[4.5], [4.5]-[8.0], and [8.0]-[24] are ideal as AGN/non-AGN
diagnostics at, respectively, z<~1, 1<~z<~2.5, and z>~2.5-3. However, when the
source redshift is unknown, these colors should be combined. We thus develop an
improved IR criterion (using Ks and IRAC bands, KI) as a new alternative at
z<~2.5. KI does not show improved completeness (50-60% overall) in comparison
to commonly used IRAC-based AGN criteria, but is less affected by non-AGN
contamination (revealing a >50-90% level of successful AGN selection). We also
propose KIM (using Ks, IRAC, and MIPS-24um bands, KIM), which aims to select
AGN hosts from local distances to as far back as the end of reionization
(0<z<~7) with reduced non-AGN contamination. However, the necessary
testing-constraints and the small control-sample sizes prevent the confirmation
of its improved efficiency at z<~2.5. Overall, KIM shows a ~30-40% completeness
and a >70-90% level of successful AGN selection. KI and KIM are built to be
reliable against a ~10-20% error in flux, are based on existing filters, and
are suitable for immediate use.
