Most high-energy solar energetic particles are believed to be accelerated at shock waves driven by coronal mass ejections (CMEs). The acceleration process strongly depends on the shock geometry and the structure of the sheath that forms behind the shock. In an effort to understand the structure and time evolution of such CME-driven shocks and their relevance to particle acceleration, we investigate the interaction of a fast CME with the ambient solar wind by means of a three-dimensional numerical ideal MHD model. Our global steady state coronal model possesses high-latitude coronal holes and a helmet streamer structure with a current sheet near the equator, reminiscent of near solar minimum conditions. Fast and slow solar winds flow at high and low latitude, respectively, and the Archimedean spiral geometry of the interplanetary magnetic field is reproduced by solar rotation. Within this model system, we drive a CME to erupt by introducing a Gibson-Low magnetic flux rope that is embedded in the helmet streamer in an initial state of force imbalance. The flux rope rapidly expands and is ejected from the corona with maximum speeds in excess of 1000 km s-1, driving a fast-mode shock from the inner corona to a distance of 1 AU. We find that the ambient solar wind structure strongly affects the evolution of the CME-driven shocks, causing deviations of the fast-mode shocks from their expected global configuration. These deflections lead to substantial compressions of the plasma and magnetic field in their associated sheath region. The sudden postshock increase in magnetic field strength on low-latitude field lines is found to be effective for accelerating particles to the GeV range.