Plasma density transition trapping is a recently purposed self-injection scheme for plasma wake-field accelerators. This technique uses a sharp downward plasma density transition to trap and accelerate background plasma electron in a plasma wake-field. This paper examines the quality of electron beams captured using this scheme in terms of emittance, energy spread, and brightness. Two-dimensional Particle-In-Cell (PIC) simulations show that these parameters can be optimized by manipulating the plasma density profile. We also develop, and support with simulations, a set of scaling laws that predict how the brightness of transition trapping beams scales with the plasma density of the system. These scaling laws indicate that transition trapping can produce beams with brightness ≥ 5x10 14 Amp/(mrad) 2 . A proof-of-principle transition trapping experiment is planned for the UCLA Neptune Laboratory in the near future. The proposed experiment and its status are described in detail.