The aim of this paper is to investigate ways to optimize the accuracy of photometric redshifts for a Supernova Acceleration Probe (SNAP)-like mission. We focus on how the accuracy of the photometric redshifts depends on the magnitude limit and signal-to-noise ratio (S/N), wavelength coverage, and the number of filters and their shapes and observed galaxy type. We use simulated galaxy catalogs constructed to reproduce observed galaxy luminosity functions from the Great Observatories Origins Deep Survey and derive photometric redshifts using a template fitting method. By using a catalog that resembles real data, we can estimate the expected number density of galaxies for which photometric redshifts can be derived. We find that the accuracy of the photometric redshifts is strongly dependent on the S/N (i.e., S/N > 10 is needed for accurate photometric redshifts). The accuracy of the photometric redshifts is also dependent on galaxy type, with smaller scatter for earlier-type galaxies. Comparing results using different filter sets, we find that including the U-band and near-IR bands is important for decreasing the fraction of outliers, i.e., "catastrophic failures." Using broad overlapping filters with resolution ~4 gives better photometric redshifts compared to narrower filters (resolution 5) with the same integration time. We find that filters with square response curves result in a slightly higher scatter, mainly due to a higher fraction of outliers at faint magnitudes. We also compare a 9-filter set to a 17-filter set, where we assume that the available exposure time per filter in the latter set is half that of the first set. We find that the 9-filter set gives more accurate redshifts for a larger number of objects and reaches higher redshift, while the 17-filter set gives better results at bright magnitudes.