With the rapid growth of congestion-sensitive and data-intensive applications, traditional settlement-free peering agreements with best-effort delivery often do not meet the QoS requirements of content providers (CPs). Meanwhile, Internet access providers (IAPs) feel that revenues from end-users are not sufficient to recoup the upgrade costs of network infrastructures. Consequently, some IAPs have begun to offer CPs a new type of peering agreement, called paid peering, under which they provide CPs with better data delivery quality for a fee. In this paper, we model a network platform where an IAP makes decisions on the peering types offered to CPs and the prices charged to CPs and end-users. We study the optimal peering schemes for the IAP, i.e., to offer CPs both the paid and settlement-free peering to choose from or only one of them, as the objective is profit or welfare maximization. Our results show that 1) the IAP should always offer the paid and settlement-free peering under the profit-optimal and welfare-optimal schemes, respectively, 2) whether to simultaneously offer the other peering type is largely driven by the type of data traffic, e.g., text or video, and 3) regulators might want to encourage the IAP to allocate more network capacity to the settlement-free peering for increasing user welfare.