We present results from constant pressure molecular-dynamics simulations for a bead-spring model of a crystallizable polymer melt. Our model has two main features, a chemically realistic intrachain rigidity and a purely repulsive interaction between nonbonded monomers. By means of intrachain and interchain structure factors we explore polymer conformation and melt structure above and below the temperature T{crys}{hom} of homogeneous crystallization. Here, we do not only determine average spatial correlations, but also site-specific correlations which depend on the position of the monomers along the polymer backbone. In the liquid phase above T{crys}{hom} we find that this site dependence can be well-accounted for by known theoretical approximations, the Koyama distribution for the intrachain structure and the polymer reference interaction site model (PRISM) for the interchain structure. This is no longer true in the semicrystalline phase. Below T{crys}{hom} short chains fully extend upon crystallization, whereas sufficiently long chains form chain-folded lamellae which coexist with amorphous regions. The structural features of these polymer crystals lead to violations of premises of the Koyama approximation or PRISM theory so that both theoretical approaches cannot be applied simultaneously. Furthermore, we find a violation of the Hansen-Verlet freezing criterion; our polymer melt crystallizes more easily than a simple liquid. This hints at the importance of the coupling between conformation (backbone rigidity) and density (packing constraints) for polymer crystallization.