Long-duration gamma-ray bursts (GRBs) are powerful tracers of star-forming galaxies. We have defined a homogeneous sub-sample of 69 Swift GRB-selected galaxies spanning a very wide redshift range. Special attention has been devoted to making the sample optically unbiased through simple and well-defined selection criteria based on the high-energy properties of the bursts and their positions on the sky. In this paper, we present the survey design and summarize the results of our observing program conducted at the ESO Very Large Telescope (VLT) aimed at obtaining the most basic properties of galaxies in this sample, including a catalog of R and Ksubs magnitudes and redshifts. Seven hosts have detections of the Ly alpha emission line and we can exclude an early indication that Ly alpha emission is ubiquitous among GRB hosts, but confirm that Ly alpha is stronger in GRB-selected galaxies than in flux-limited samples of Lyman break galaxies.