  Context: Combining high-contrast imaging with medium- or high-resolution
integral field spectroscopy has the potential to boost the detection rate of
exoplanets, especially at small angular separations. Furthermore, it
immediately provides a spectrum of the planet that can be used to characterise
its atmosphere. The achievable spectral resolution, wavelength coverage, and
FOV of such an instrument are limited by the number of available detector
pixels. Methods: The trade-offs are studied through end-to-end simulations of a
typical high-contrast imaging instrument, analytical considerations, and
atmospheric retrievals. The results are then validated with archival
VLT/SINFONI data of the planet beta Pictoris b. Results: We show that molecular
absorption spectra generally have decreasing power towards higher spectral
resolution and that molecule mapping is already powerful for moderate
resolutions (R>300). When choosing between wavelength coverage and spectral
resolution for a given number of spectral bins, it is best to first increase
the spectral resolution until R~2,000 and then maximise the bandwidth within an
observing band. We find that T-type companions are most easily detected in the
J/H band through methane and water features, while L-type companions are best
observed in the H/K band through water and CO features. Such an instrument does
not need to have a large FOV, as most of the gain in contrast is obtained in
the speckle-limited regime close to the star. We show that the same conclusions
are valid for the constraints on atmospheric parameters such as the C/O ratio,
metallicity, surface gravity, and temperature, while higher spectral resolution
(R~10,000) is required to constrain the radial velocity and spin of the planet.
