We investigate the Fermi Large Area Telescope gamma-ray and 15 GHz Very Long Baseline Array radio properties of a joint gamma-ay and radio-selected sample of active galactic nuclei (AGNs) obtained during the first 11 months of the Fermi mission (2008 August 4-2009 July 5). Our sample contains the brightest 173 AGNs in these bands above declination -30 degrees during this period, and thus probes the full range of gamma-ray loudness (gamma-ray to radio band luminosity ratio) in the bright blazar population. The latter quantity spans at least 4 orders of magnitude, reflecting a wide range of spectral energy distribution (SED) parameters in the bright blazar population. The BL Lac objects, however, display a linear correlation of increasing gamma-ray loudness with synchrotron SED peak frequency, suggesting a universal SED shape for objects of this class. The synchrotron self-Compton model is favored for the gamma-ray emission in these BL Lac objects over external seed photon models, since the latter predict a dependence of Compton dominance on Doppler factor that would destroy any observed synchrotron SED-peak-gamma-ray-loudness correlation. The high-synchrotron peaked (HSP) BL Lac objects are distinguished by lower than average radio core brightness temperatures, and none display large radio modulation indices or high linear core polarization levels. No equivalent trends are seen for the flat-spectrum radio quasars (FSRQs) in our sample. Given the association of such properties with relativistic beaming, we suggest that the HSP BL Lac objects have generally lower Doppler factors than the lower-synchrotron peaked BL Lac objects or FSRQs in our sample.