In cooperative P2P Web caching if the Web cache first receiving a request does not have the document in its memory, it starts searching for it in other nearby cooperating Web caches, retrieving and sending it to the client before contacting the origin (content) server. The advantages of cooperative caching are clear: it reduces the network bandwidth consumption, actual traffic on the origin servers, and average latency experienced by the clients of these caches. Although several cooperative caching protocols have been proposed, few studies have examined how to select the best proxy server that would offer the best response time to a Web client. In this paper, we propose to dynamically measure the data transfer rates between proxy servers to facilitate efficient server selection. However, the main goal of the paper is to study the performance benefits of integrating efficient server selection mechanism. Our analysis shows that attempts to choose the fastest server can be hugely beneficial as file transfer time is significantly better as compared to conventional cooperative proxy mechanisms where selection is largely random.