We report on VERITAS very high energy (VHE; E ≥ 100 GeV) observations of six blazars selected from the Fermi Large Area Telescope First Source Catalog (1FGL). The gamma-ray emission from 1FGL sources was extrapolated up to the VHE band, taking gamma-ray absorption by the extragalactic background light into account. This allowed the selection of six bright, hard-spectrum blazars that were good candidate TeV emitters. Spectroscopic redshift measurements were attempted with the Keck Telescope for the targets without Sloan Digital Sky Survey spectroscopic data. No VHE emission is detected during the observations of the six sources described here. Corresponding TeV upper limits are presented, along with contemporaneousFermi observations and non-concurrent Swift UVOT and X-Ray Telescope data. The blazar broadband spectral energy distributions (SEDs) are assembled and modeled with a single-zone synchrotron self-Compton model. The SED built for each of the six blazars shows a synchrotron peak bordering between the intermediate- and high-spectrum-peak classifications, with four of the six resulting in particle-dominated emission regions.