We present results from VLBI observations of 24 of the 25 lobe-dominated quasars (LDQs) in the 3CR complete sample and from optical spectrophotometry of 14 of these objects. The VLBI observations were made with a variety of arrays—most recently the Very Long Baseline Array—at frequencies ranging from 5 to 22 GHz during the period 1981–1997. The optical spectra were obtained with the Hale 200 inch (5 m) telescope at Palomar Observatory, using the blue and red CCDs of the Double Spectrograph, between 1984 and 1992. The radio nuclei range in strength over nearly 3 orders of magnitude, from ∼0.9 Jy down to ∼3 mJy, and were imaged at typical resolutions of ∼0.5–1.0 mas and sensitivities of ∼0.1–0.2 mJy beam-1. All 24 LDQs show detectable radio structure in their nuclei. All 19 objects for which VLBI images could be made show one-sided nuclear jets, often several milliarcseconds in length and significantly curved, on the same side of the compact core as the one-sided large-scale jets seen on Very Large Array images. No counterjets were observed; jet-to-counterjet ratios that virtually all exceed ∼10 suggest that these objects are all oriented within ∼70° to the line of sight. For the 10 sources in which parsec-scale jet speeds could be estimated, the well-defined motions range from ≲h-1c to ∼4h-1c; some ambiguous cases might allow for motions as fast as ∼8h-1c, even then they are not indicative of bulk Lorentz factors, γ, in excess of ∼10h-1 (H0 = 100h km s-1 Mpc-1, q0 = 0.5). While the present distribution of jet speeds is consistent with random orientations, it is more easily accomodated by a restricted range of orientations. Evidence for slower jet speeds and larger apparent bends close to the core support the concept of a "transition" zone in the inner few parsecs of these jets. There are significant correlations among the prominences of the cores and jets, relative jet length, maximum jet deflection angles, and variability amplitude, as well as possible trends involving jet speed and strength of compact jet knots; furthermore, these objects tend to exhibit flat-spectrum cores and steep-spectrum jets. These results are all consistent with orientation-dependent relativistic beaming effects and unification of core- and lobe-dominated quasars. We have also defined a new postulated measure of orientation, based on both prominence of the radio nucleus and projected linear size, that correlates very well with properties predicted to have strong orientation dependence on beaming models. Finally, we confirm earlier studies demonstrating an anticorrelation between the prominence of the radio nucleus and the width of broad Mg II λ2798 optical emission lines; we also extend this result to C III] λ1909 and, more generally, to all broad lines by simple scaling and normalization methods. This relationship suggests a restricted range of orientations for LDQs, and that the broad-line clouds may have a flattened distribution associated with the accretion zone surrounding a central supermassive black hole.