The increased interest in understanding the thermodynamic activity in finite systems such as nanotechnological and biological systems has initiated numerous studies in interdisciplinary research. The properties and functions of these systems are inevitably connected to their geometric structures. However, due to finite-size and surface effects, conventional canonical statistical analysis fails to locate unique structural transition points for such systems. By considering integrated autocorrelation times of energetic and structural quantities, generalizing microcanonical inflection-point analysis, and introducing conformational analysis methods, we aim at developing more systematic and general approaches to the study of systems of finite size. To elucidate the power of these methods, we investigate coarse-grained lattice and off-lattice homopolymers by means of Monte Carlo importance sampling methods such as Metropolis, parallel tempering, and a parallel version of multicanonical sampling.