We investigate how the properties of spiral arms relate to other fundamental galaxy properties, including bars and disc breaks. We use previously published measurements of those properties, and our own measurements of arm and bar contrasts for a large sample of galaxies, using 3.6 mu m images from the Spitzer Survey of Stellar Structure in Galaxies. Flocculent galaxies are clearly distinguished from other spiral arm classes, especially by their lower stellar mass and surface density. Multi-armed and grand-design galaxies are similar in most of their fundamental parameters, excluding some bar properties and the bulge-to-total ratio. Based on these results, we revisit the sequence of spiral arm classes, and discuss classical bulges as a necessary condition for standing spiralwave modes in grand-design galaxies. We find a strong correlation between bulge-to-total ratio and bar contrast, and a weaker correlation between arm and bar contrasts. Barred and unbarred galaxies exhibit similar arm contrasts, but the highest arm contrasts are found exclusively in barred galaxies. Interestingly, the bar contrast, and its increase from flocculent to grand-design galaxies, is systematically more significant than that of the arm contrast. We corroborate previous findings concerning a connection between bars and disc breaks. In particular, in grand-design galaxies, the bar contrast correlates with the normalized disc break radius. This does not hold for other spiral arm classes or the arm contrast. Our measurements of arm and bar contrast and radial contrast profiles are publicly available.