  Galaxies with stellar masses near M* contain the majority of stellar mass in
the universe, and are therefore of special interest in the study of galaxy
evolution. The Milky Way (MW) and Andromeda (M31) have present day stellar
masses near M*, at 5x10^10 Msol (MW-mass) and 10^11 Msol (M31-mass). We study
the typical progenitors of these galaxies using ZFOURGE, a deep medium-band
near-IR imaging survey, which is sensitive to the progenitors of these galaxies
out to z~3. We use abundance-matching techniques to identify the main
progenitors of these galaxies at higher redshifts. We measure the evolution in
the stellar mass, rest-frame colors, morphologies, far-IR luminosities, and
star-formation rates combining our deep multiwavelength imaging with near-IR
HST imaging from CANDELS, and far-IR imaging from GOODS-H and CANDELS-H. The
typical MW-mass and M31-mass progenitors passed through the same evolution
stages, evolving from blue, star-forming disk galaxies at the earliest stages,
to redder dust-obscured IR-luminous galaxies in intermediate stages, and to
red, more quiescent galaxies at their latest stages. The progenitors of the
MW-mass galaxies reached each evolutionary stage at later times (lower
redshifts) and with stellar masses that are a factor of 2-3 lower than the
progenitors of the M31-mass galaxies. The process driving this evolution,
including the suppression of star-formation in present-day M* galaxies requires
an evolving stellar-mass/halo-mass ratio and/or evolving halo-mass threshold
for quiescent galaxies. The effective size and star-formation rates imply that
the baryonic cold-gas fractions drop as galaxies evolve from high redshift to
z~0 and are strongly anticorrelated with an increase in the S\'ersic index.
Therefore, the growth of galaxy bulges in M* galaxies corresponds to a rapid
decline in the galaxy gas fractions and/or a decrease in the star-formation
efficiency.
