We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. We describe K-theoretical conditions that give rise to prime, RFD, and MF reduced crossed products. In the presence of sufficiently many projections we associate to each noncommutative C*-system (A,G) a type semigroup S(A,G) which reflects much of the spirit of the underlying action. Inspired by the work of Rørdam and Sierakowski we characterize purely infinite, as well as stably finite, crossed products by means of the infinite or rather finite nature of this semigroup.