The relative contribution of baryons and dark matter to the inner regions of spiral galaxies provides critical clues to their formation and evolution, but it is generally difficult to determine. For spiral galaxies that are strong gravitational lenses, however, the combination of lensing and kinematic observations can be used to break the disc–halo degeneracy. In turn, such data constrain fundamental parameters such as (i) the mass density profile slope and axial ratio of the dark matter halo, and by comparison with dark matter-only numerical simulations the modifications imposed by baryons; (ii) the mass in stars and therefore the overall star formation efficiency, and the amount of feedback; (iii) by comparison with stellar population synthesis models, the normalization of the stellar initial mass function. In this first paper of a series, we present a sample of 16 secure, one probable and six possible strong lensing spiral galaxies, for which multiband high-resolution images and rotation curves were obtained using the Hubble Space Telescope and Keck II telescope as part of the Sloan WFC Edge-on Late-type Lens Survey (SWELLS). The sample includes eight newly discovered secure systems. We characterize the sample of deflector galaxies in terms of their morphologies, structural parameters and stellar masses. We find that the SWELLS sample of secure lenses spans a broad range of morphologies (from lenticular to late-type spiral), spectral types (quantified by Hα emission) and bulge to total stellar mass ratio (0.22–0.85), while being limited to M* > 1010.5 M⊙. The SWELLS sample is thus well suited for exploring the relationship between dark and luminous matter in a broad range of galaxies. We find that the deflector galaxies obey the same size–mass relation as that of a comparison sample of elongated non-lens galaxies selected from the Sloan Digital Sky Survey. We conclude that the SWELLS sample is consistent with being representative of the overall population of high-mass high-inclination discy galaxies.