  We present detailed studies of the high-field magnetoresistance of the
layered organic metal $\kappa$-(BETS)$_2$\-Mn\-[N(CN)$_2$]$_3$ under a pressure
slightly above the insulator-metal transition. The experimental data are
analysed in terms of the Fermi surface properties and compared with the results
of first-principles band structure calculations. The calculated size and shape
of the inplane Fermi surface are in very good agreement with those derived from
Shubnikov-de Haas oscillations as well as the classical angle-dependent
magnetoresistance oscillations. A comparison of the experimentally obtained
effective cyclotron masses with the calculated band masses reveals electron
correlations significantly dependent on the electron momentum. The momentum- or
band-dependent mobility is also reflected in the behavior of the classical
magnetoresistance anisotropy in a magnetic field parallel to layers. Other
characteristics of the conducting system related to interlayer charge transfer
and scattering mechanisms are discussed based on the experimental data. Besides
the known high-field effects associated with the Fermi surface geometry, new
pronounced features have been found in the angle-dependent magnetoresistance,
which might be caused by coupling of the metallic charge transport to a
magnetic instability in proximity to the metal-insulator phase boundary.
