In many bacterial species, the protein FtsZ forms a cytoskeletal ring that marks the future division site and scaffolds the division machinery. In rod-shaped bacteria, most frequently membrane-attached FtsZ rings or ring fragments are reported and occasionally helices. By contrast, axial FtsZ clusters have never been reported. In this paper, we investigate theoretically how dynamic FtsZ aggregates align in rod-shaped bacteria. We study systematically different physical mechanisms that affect the alignment of FtsZ polymers using a computational model that relies on autocatalytic aggregation of FtsZ filaments at the membrane. Our study identifies a general tool kit of physical and geometrical mechanisms by which rod-shaped cells align biopolymer aggregates. Our analysis compares the relative impact of each mechanism on the circumferential alignment of FtsZ as observed in rod-shaped bacteria. We determine spontaneous curvature of FtsZ polymers and axial confinement of FtsZ on the membrane as the strongest factors. Including Min oscillations in our model, we find that these stabilize axial and helical clusters on short time scales, but promote the formation of an FtsZ ring at the cell middle at longer times. This effect could provide an explanation to the long standing puzzle of transiently observed oscillating FtsZ helices in Escherichia coli cells prior to cell division.