Entropy sampling Monte Carlo, the replica method, and the classical Metropolis scheme were applied in numerical studies of the collapse transition in a simple face-centered cubic lattice polymer. The force field of the model consists of pairwise, contact-type, long-range interactions and a short-range potential based on the beta-sheet definition assumed in the model. The ability to find the lowest energy conformation by various Monte Carlo methods and the computational cost associated with each was examined. It is shown that all of the methods generally provide the same picture of the collapse transition. However, the most complete thermodynamic description of the transition derives from the results of entropy sampling Monte Carlo simulations, but this is the most time-consuming method. The replica method is shown to be the most effective and efficient in searching for the lowest energy conformation. The possible consequences of these findings for the development of simulation strategies for the folding of model proteins are discussed briefly.