You choice of anion when building your star depends on how you've designed your formulation. Carbonates and oxides are used to make a star (or say, fountain composition) less brisant, to slow down a reaction that's going to fast for people to see it. On the other hand, the composition needs some oxidizer, and sometimes the colored salt is used to help, for example, bursting charge can be made with barium nitrate or barium chlorate, that's what gives flash powder its flash.