The correlations between structure and dynamics in free and surface-immobilized polymers were investigated via Langevin dynamics simulations of a free-jointed homopolymer. A detailed analysis was performed for a polymer in free solution and a polymer attached to a surface. The cases of repulsive and attractive Surfaces, as well as poor and good solvents, were considered. The analysis focuses oil properties that are particularly relevant to single molecule measurements, namely: (1) the distribution of end-to-end distance, (2) the correlations between the conformational structure and the time scale of its motion, (3) the correlations. at equilibrium, between the end-to-end distance and its displacement, and (4) the correlation between the initial coil conformation and the collapse pathway into the globular state. The differences and similarities between this model and a previously considered model of a protein, with two-state folding kinetics and a well-defined native state, are also discussed.