Cloud computing is one of the most significant latest efforts in the field of information technology, which may change the way how information services are provisioned. In a Cloud environment, different types of resources need to be virtualized as a collection of Cloud services using virtualization technology. End-users in the Cloud are usually provided with customized Cloud services that involve not only different kinds of computing services but also the networks interconnecting those computing services. Therefore, a set of Cloud computing services and the networking services should be modeled as a composite customized Cloud service. In this paper, we present an improved model for Cloud service provisioning based on our previous Network-Cloud proposal, and propose a procedure with several QoS-aware service selection algorithms for composing different services offered by a Cloud. Our analysis with numerical experiments show that the presented algorithms can select services appropriately that deal with different requirements of service provisioning.