  We present the SINS survey with SINFONI of high redshift galaxies. With 80
objects observed and 63 detected, SINS is the largest survey of spatially
resolved gas kinematics, morphologies, and physical properties of star-forming
galaxies at z~1-3. We describe the selection of the targets, the observations,
and the data reduction. We then focus on the "SINS Halpha sample" of 62
rest-UV/optically-selected sources at 1.3<z<2.6 for which we targeted primarily
the Halpha and [NII] emission lines. Only 30% of this sample had previous
near-IR spectroscopic observations. As a whole, the SINS Halpha sample covers a
reasonable representation of massive log(M*/Msun)>~10 star-forming galaxies at
z~1.5-2.5, with some bias towards bluer systems compared to pure K-selected
samples due to the requirement of secure optical redshift. The sample spans two
orders of magnitude in stellar mass and in absolute and specific star formation
rates, with median values of approximately log(M*/Msun) = 10.5, 70 Msun/yr, and
3/Gyr. The ionized gas distribution and kinematics are spatially resolved on
scales ranging from 1.5 kpc for adaptive optics assisted observations to
typically 4-5 kpc for seeing-limited data. The Halpha morphologies tend to be
irregular and/or clumpy. About one-third are rotation-dominated yet turbulent
disks, another third comprises compact and velocity dispersion-dominated
objects, and the remaining galaxies are clear interacting/merging systems; the
fraction of rotation-dominated systems increases among the more massive part of
the sample. The Halpha luminosities and equivalent widths suggest on average
roughly twice higher dust attenuation towards the HII regions relative to the
bulk of the stars, and comparable current and past-averaged star formation
rates. [Abridged]
