Ultrasound computed tomography (USCT) is an emerging modality to image the acoustic properties of the breast tissue for cancer diagnosis. With the need of improving the diagnostic accuracy of USCT, while maintaining the cost low, recent research is mainly focused on improving (1) the reconstruction methods and (2) the acquisition systems. D-optimal sequential experimental design (D-SOED) offers a method to integrate these aspects into a common systematic framework. The transducer configuration is optimized to minimize the uncertainties in the estimated model parameters, and to reduce the time to solution by identifying redundancies in the data. This work presents a formulation to jointly optimize the experiment for transmission and reflection data and, in particular, to estimate the speed of sound and reflectivity of the tissue using either ray-based or wave-based imaging methods. Uncertainties in the parameters can be quantified by extracting properties of the posterior covariance operator, which is analytically computed by linearizing the forward problem with respect to the prior knowledge about parameters. D-SOED is first introduced by an illustrative toy example, and then applied to real data. This shows that the time to solution can be substantially reduced, without altering the final image, by selecting the most informative measurements.