The fundamental performance of several TBCC engines is investigated from Mach 0-5. The primary objective of this research is the direct comparison of several TBCC engine concepts, ultimately determining the most suitable option for the first stage of a two-state-to-orbit launch vehicle. TBCC performance models are developed and optimized. A hybrid optimizer is developed, combining the global accuracy of probabilistic optimization with the local efficiency of gradient-based optimization. Trade studies are performed to determine the sensitivity of TBCC performance to various design variables and engine parameters. The optimization is quite effective, producing results with less than 1% error from optimizer repeatability. The turbine-bypass engine (TBE) provides superior specific impulse performance. The hydrocarbon-fueled gas-generator air turborocket and hydrogen-fueled expander-cycle air turborocket are also competitive because they may provide greater thrust-to-weight than the TBE, but require some engineering problems to be addressed before being fully developed.