  We present and characterize a sample of 20 nearby Seyfert galaxies selected
for having BAT 14--195keV luminosities $L_X \ge 10^{41.5}$ erg s$^{-1}$,
redshift $z\le$0.015, being accessible for observations with the Gemini
Near-Infrared Field Spectrograph (NIFS) and showing extended
[OIII]$\lambda$5007 emission. Our goal is to study Active Galactic Nuclei (AGN)
feeding and feedback processes from near-infrared integral-field spectra, that
include both ionized (HII) and hot molecular (H$_2$) emission. This sample is
complemented by other 9 Seyfert galaxies previously observed with NIFS. We show
that the host galaxy properties (absolute magnitudes $M_B$, $M_H$, central
stellar velocity dispersion and axial ratio) show a similar distribution to
those of the 69 BAT AGN. For the 20 galaxies already observed, we present
surface mass density ($\Sigma$) profiles for HII and H$_2$ in their inner
$\sim$500 pc, showing that HII emission presents a steeper radial gradient than
H$_2$. This can be attributed to the different excitation mechanisms:
ionization by AGN radiation for HII and heating by X-rays for H$_2$. The mean
surface mass densities are in the range ($0.2\le \Sigma_{HII} \le
35.9$)M$_\odot$pc$^{-2}$, and ($0.2\le \Sigma_{H2} \le
13.9$)$\times10^{-3}$M$_\odot$pc$^{-2}$, while the ratios between the HII and
H$_2$ masses range between $\sim$200 to 8000. The sample presented here will be
used in future papers to map AGN gas excitation and kinematics, providing a
census of the mass inflow and outflow rates and power as well as their relation
with the AGN luminosity.
