We report on the design, fabrication and analysis of vertical-cavity surface-emitting transistor-lasers (T-VCSELs) based on the homogeneous integration of an InGaAs/GaAs VCSEL and an AlGaAs/GaAs pnp-heterojunction bipolar transistor (HBT). Epitaxial regrowth confinement, modulation doping, intracavity contacting and non-conducting mirrors are used to ensure a low-loss structure, and a variety of design variations are investigated for a proper internal biasing and current injection to ensure a wide operating range. Optimized devices show mW-range output power, mA-range base threshold current and high-temperature operation to at least 60°C with the transistor in its active mode of operation for base currents well beyond threshold. Current confinement schemes based on pnp-blocking layers or a buried tunnel junction are investigated as well as asymmetric current injection for reduced extrinsic resistances.