One of the crucial steps in the viral replication cycle is the self-assembly of its protein shell. Typically, each native virus adopts a unique architecture, but the coat proteins of many viruses have the capability to self-assemble in vitro into different structures by changing the assembly conditions. However, the mechanisms determining which of the possible capsid shapes and structures is selected by a virus are still not well-known. We present a coarse-grained model to analyze and understand the physical mechanisms controlling the size and structure selection in the assembly of empty viral capsids. Using this model and Monte Carlo simulations, we have characterized the phase diagram and stability of T = 1,3,4,7 and snub cube shells. In addition, we have studied the tolerance of different shells to changes in physical parameters related to ambient conditions, identifying possible strategies to induce misassembly or failure. Finally, we discuss the factors that select the shape of a capsid as spherical, faceted, elongated, or decapsidated. Our model sheds important light on the ingredients that control the assembly and stability of viral shells. This knowledge is essential to get capsids with well-defined size and structure that could be used for promising applications in medicine or bionanotechnology.