Spatially resolved images of debris disks are necessary to determine disk geometric properties and the scattering phase function (SPF) which quantifies the brightness of the scattered light as a function of phase angle. The combination of high contrast and high angular resolution imaging is required to obtain these unique and important probes of debris disks, and we report on an adaptive optics 1.25-2.2 micron imaging survey of 17 high infrared excess debris disks observed with a Gemini Large and Long Program (LLP) utilizing the Gemini Planet Imager (GPI). The sample is composed of stars ranging in ages of 10-500 Myr and spectral types A-G. We explore quantitatively whether most debris disks are characterized by a similar SPF as suggested by previous studies. The SPF depends on important dust properties such as grain size distribution and porosity that are linked to the frequency of collisions that generate small grains and promote compactification of grains. To date, only a very limited number of SPF measurements have been made, and there has been no uniform study modeling the geometry and SPFs of even a modest sample of debris disks using a consistent methodology. Additionally, we investigate and compare geometric properties of these systems such as radial extent and vertical thickness. By determining the best-fitting models for these systems, the disk scale height, SPFs, and dust properties can be estimated and compared between host stars of different ages and masses, as well as examples from the Solar System.