This paper explores the design trade-offs required for an Internet transport protocol to effectively support web access. It identifies a set of distinct transport mechanisms and explores their use with a focus on multistreaming. The mechanisms are studied using a practical methodology that utilise the range of transport features provided by TCP and SCTP. The results demonstrate the relative benefit of key transport mechanisms and analyse how these impact web access performance. Our conclusions help identify the root causes of performance impairments and suggest appropriate choices guiding the design of a web transport protocol. Performing this analysis at the level of component transport mechanisms enables the results to be utilised in the design of new transport protocols, such as IETF QUIC.