Carrier dynamics in GaAs-based photoconductive terahertz (THz) sources is investigated using Monte Carlo techniques to optimize the emitted THz transients. A self-consistent Monte Carlo-Poisson solver is developed for the spatio-temporal carrier transport properties. The screening contributions to the THz radiation associated with the Coulomb and radiation fields are obtained self-consistently by incorporating the three-dimensional Maxwell equations into the solver. In addition, the enhancement of THz emission by a large trap-enhance field (TEF) near the anode in semi-insulating (SI) photoconductors is investigated. The transport properties of the photoexcited carriers in photoconductive THz sources depend markedly on the initial spatial distribution of those carriers. Thus, considerable control of the emitted THz spectrum can be attained by judiciously choosing the optical excitation spot shape on the photoconductor, since the carrier dynamics that provide the source of the THz radiation are strongly affected by the ensuing screenings. The screening contributions due to the Coulomb and radiation parts of the electromagnetic field acting back on the carrier dynamics are distinguished. The dominant component of the screening field crosses over at an excitation aperture size with full width at half maximum (FWHM) of ~100 um for a range of reasonable excitation levels. In addition, the key mechanisms responsible for the TEF near the anode of SI photoconductors are elucidated in detail. For a given optical excitation power, an enhancement of THz radiation power can be obtained using a maximally broadened excitation aperture in the TEF area elongated along the anode due to the reduction in the Coulomb and radiation screening of the TEF.