In general, I would use Aperture Priority and adjust the aperture to suit my intended desire for the image, letting the camera choose the shutter-speed. But, with your flash on the camera will almost always choose 1/60. If that is stopping the action, then great. If not, go to manual, increase the shutter speed and let the flash automatically increase it's power to do the rest.
If the ceilings allow for it, bounce off them with a diffuser dome on the speed light. (what speed light do you have?)
With those lenses, and assuming it will not be very bright indoors I think the flash will be a must. Using some kind of diffuser or bounce card will really help. Do you know any details about the place? How high are the ceilings, what color are they? Again, what flash are you using? (That will help me tailor the advice)