The satellite network is useful in various applications because of its coverage, broadcast capability, costs independent of the distance, and easy deployment. Recently, thanks to the advanced technologies in the satellite communication, the high throughput satellite system with mesh connections has been applied to the Internet backbone. In this paper, we propose a practical overall design of the satellite network to provide Internet services with quality of service (QoS) support via the satellite network. In the proposed design, we consider two service types such as delay-tolerance and delay-sensitive services allowing the long propagation delay of the satellite link. Since it is crucial to evaluate the user satisfaction in the application layer for various environments to provide the QoS support, we also define the performance metrics for the user satisfaction and derive the major factors to be considered in the QoS policy. The results of the performance evaluation show that there are factors such as the traffic load and burstiness in the QoS policy for the delay-tolerance service with volume-based dynamic capacity in the satellite network. For the delay-sensitive service with rate-based dynamic capacity, it is additionally indicated that it is important for the estimation of effective data transmission rate to guarantee the QoS. Furthermore, it is shown that the small data size has an effect on the slight reduction of the QoS performance in the satellite network.