Cloud-based Radio Access Network (C-RAN) is a promising architecture for future cellular networks, in which Baseband Units (BBUs) are placed at a centralized location, with capacity-constrained fronthaul connected to multiple distributed Remote Radio Units (RRHs) that are far away from the BBUs. The centralization of signal processing enables the flexibility for coordinated multi-point transmission (CoMP) to meet high traffic demand of users. We investigate how to jointly optimize CoMP-cell selection and base station resource allocation so as to enhance the quality of service (QoS), subject to the fronthaul capacity constraint in orthogonal frequency-division multiple access (OFDMA) based C-RAN. The problem is proved to be NP-hard in this paper. To deal with the computational complexity, we derive a partial optimality condition as the foundation for designing a cell-selection algorithm. Besides, we provide a solution method of the optimum of the time-frequency resource allocation problem without loss of fairness on the QoS enhancement of all users. The simulations show good performance of the proposed algorithms for jointly optimizing the cell selection and resource allocation in a C-RAN, with respect to QoS.