In this paper, we address the problem of efficiently streaming a set of heterogeneous videos from a remote server through a proxy to multiple asynchronous clients so that they can experience playback with low startup delays. We develop a technique to analytically determine the optimal proxy prefix cache allocation to the videos that minimizes the aggregate network bandwidth cost. We integrate proxy caching with traditional serverbased reactive transmission schemes such as batching, patching and stream merging to develop a set of proxy-assisted delivery schemes. We quantitatively explore the impact of the choice of transmission scheme, cache allocation policy, proxy cache size, and availability of unicast versus multicast capability, on the resultant transmission cost. Our evaluations show that even a relatively small prefix cache (10%-20% of the video repository) is sufficient to realize substantial savings in transmission cost. We find that carefully designed proxy-assisted reactive transmission schemes can produce significant cost savings even in predominantly unicast environments such as the Internet.