Blurred movement means a slow shutter, so you want the shutter as fast as possible - shutter priority in camera terms.
Then I'd keep the ISO up around 400 all the time (unless a night shot is so dark that you need it higher). Even in sunlight. a shutter speed of 1/24000 should be enough that you'd need to open the lens all the way (f1.5).
Use the lens opening and EV to set the exposure. But ... if you need depth of field (child near, dog far, that sort of thing), you'll hve to stop the lens down, so play with the ISO to make up for the lower light coming in.
Photography is photography, whether it's a $50 phone camera or a $5,000 Hasselblad. Larger lens opening fives you more light but less depth of field. Faster shutter stops motion but gives you less light. Higher ISO, whether it's a higher ISO film or a higher ISO setting, "sees" better with less light. (The only difference is that in a digital camera, higher ISO means possible graininess, so don't get ridiculous just because the camera can get good pictures when it's so dark that you can't see.)