  We report ballistic transport commensurability minima in the
magnetoresistance of $\nu =3/2$ composite fermions (CFs). The CFs are formed in
high-quality two-dimensional electron systems confined to wide GaAs quantum
wells and subjected to an in-plane, unidirectional periodic potential
modulation. We observe a slight asymmetry of the CF commensurability positions
with respect to $\nu=3/2$, which we explain quantitatively by comparing three
CF density models and concluding that the $\nu=3/2$ CFs are likely formed by
the minority carriers in the upper energy spin state of the lowest Landau
level. Our data also allow us to probe the shape and size of the CF Fermi
contour. At a fixed electron density of $\simeq 1.8 \times 10^{11}$ cm$^{-2}$,
as the quantum well width increases from 30 to 60 nm, the CFs show increasing
spin-polarization. We attribute this to the enhancement of the Zeeman energy
relative to the Coulomb energy in wider wells where the latter is softened
because of the larger electron layer thickness. The application of an
additional parallel magnetic field ($B_{||}$) leads to a significant distortion
of the CF Fermi contour as $B_{||}$ couples to the CFs' out-of-plane orbital
motion. The distortion is much more severe compared to the $\nu=1/2$ CF case at
comparable $B_{||}$. Moreover, the applied $B_{||}$ further spin-polarizes the
$\nu=3/2$ CFs as deduced from the positions of the commensurability minima.
