We present an overview of the GHOSTS survey, the largest study to date of the resolved stellar populations in the outskirts of disk galaxies. The sample consists of 14 disk galaxies within 17 Mpc, whose outer disks and halos are imaged with the Hubble Space Telescope Advanced Camera for Surveys (ACS). In the first paper of this series, we describe the sample, explore the benefits of using resolved stellar populations, and discuss our ACS F606W and F814W photometry. We use artificial star tests to assess completeness and use overlapping regions to estimate photometric uncertainties. The median depth of the survey at 50% completeness is 2.7 mag below the tip of the red giant branch (TRGB). We comprehensively explore and parameterize contamination from unresolved background galaxies and foreground stars using archival fields of high-redshift ACS observations. Left uncorrected, these would account for 10(0.65xF814W-19.0) detections per mag per arcsec(2). We therefore identify several selection criteria that typically remove 95% of the contaminants. Even with these culls, background galaxies are a significant limitation to the surface brightness detection limit which, for this survey, is typically V similar to 30 mag arcsec(-2). The resulting photometric catalogs are publicly available and contain some 3.1 million stars across 76 ACS fields, predominantly of low extinction. The uniform magnitudes of TRGB stars in these fields enable galaxy distance estimates with 2%-7% accuracy.