The plants you choose probably won't make much difference in water storage during storms because they can't absorb water fast enough. The soil and mulch can absorb water quickly, but unless there is a very deep layer of dry soil and mulch, a rain storm can saturate it in minutes.
I don't know what type of environment you are working in, but I can't think of an environment where the plants themselves can make much difference reducing storm runoff. Dry soil material (if stabilized by plant roots so it does not wash away) can absorb some water and slow runoff at the start of rain events, but after it gets saturated overland flow will quickly carry away all the subsequent rain.
I also don't know what your goal is. If your goal is to retain as much rainwater as possible, a holding basin might be required. If you just want to soak up the rain from small rain events, building up organic material and loose soil will help. Any plants that grow well can stabilize the soil material and intercept the raindrops to provide some erosion protection.