As Mobile Network Operators (MNOs) are shifting towards Cloud-Radio Access Network (C-RAN), they have to upgrade their infrastructure to not only support higher processing capacities but also to be more resilient. We consider the problem where a MNO is faced with the choice of selecting virtualized Baseband Units (BBUs) from various cloud service providers, that are each characterized with distinct failure probabilities and prices. We propose to solve the BBU selection problem, formulated as an Integer Linear Program (ILP) subject to BBU capacity and virtualization cost using the Branch-and-Price algorithm. We present several schemes depicting which optimization goal the MNO can foster the most: BBU processing power minimization, resiliency, traffic handling or all. Simulation results demonstrate the good performance of our algorithm to solve the BBU selection problem for all schemes, while also emphasizing the advantages of a particular one that can realize more than 10% in virtualization cost savings.