As Frog said, the key major component to how fast you can shoot will depend significantly more on the lens you use than anything else. When 1/120th shutter works on f/5.6, 1/500th can be achieved at f/2.8. Hence, f/2.8 and faster only for action shots.

The other factor you should consider is focus speed, which has a variety of contributing factors depending on system and lens. Faster lens will always offer faster autofocus, they let more light in, the sensors can find contrast quicker.

Anyway, bottom line, get a fast lens, and pay attention to AF performance in the DSLR bodies you look into.