Any of the current DSLR's will certainly capture action without significant shutter lag.
Lens wise, it depends upon the kind of action.
If you are shooting basketball from just behind the backboard, then a lens like the 17-55 mm f/2.8 or 24-70 mm f/2.8 if using a FF camera.
Field games or when shooting any kind of racing, a 200-400 mm f/4, 400 mm f.2.8 or 600 mm f/4 are the lenses of choice