We assemble and observe a sample of poor galaxy systems that is suitable for testing N-body simulations of hierarchical clustering and other dynamical halo models. We (1) determine the parameters of the density profile ρ(r) and the velocity dispersion profile σ_p(R), (2) separate emission-line galaxies from absorption-line galaxies, examining the model parameters and as a function of spectroscopic type, and (3) for the best-behaved subsample, constrain the velocity anisotropy parameter, β, which determines the shapes of the galaxy orbits. Our sample consists of 20 systems, 12 of which have extended X-ray emission in the ROSAT All-Sky Survey. We measure the 877 optical spectra of galaxies brighter than m_R≈15.4 within 1.5 h^-1 Mpc of the system centers (we take H₀=100 h km s^-1 Mpc^-1). Thus, we sample the system membership to a radius typically three times larger than other recent optical group surveys. The average system population is 30 galaxies, and the average line-of-sight velocity dispersion is ≈300 km s^-1. The Navarro, Frenk, & White universal profile and the Hernquist model both provide good descriptions of the spatial data. In most cases an isothermal sphere is ruled out. Systems with declining σ_p(R) are well-matched by theoretical profiles in which the star-forming galaxies have predominantly radial orbits (β>0); many of these galaxies are probably falling in for the first time. There is significant evidence for spatial segregation of the spectroscopic classes regardless of σ_p(R).