Magic-size nanoclusters and -particles have versatile technological applications that rely on their high degree of monodispersity, in particular in connection with strongly size-dependent physical properties. The mechanisms that lead to the size-limited synthesis of nano-assemblies and the underlying interplay between thermodynamic and kinetic factors are still often mysterious. By performing numerical simulations of particles modeled via simple, isotropic interactions, we investigate the growth behavior and structural characteristics of particles that exhibit highly monodisperse assemblies. We study size-selective behavior during assembly due to competing interactions that rely on different mechanisms: both short-range attraction and long-range repulsion, as well as structure-specific processes. Our studies reveal fundamental principles that we believe can be applied to the targeted design of size-specific nanomaterial synthesis pathways.