I used to default to whatever shutter speed a semi-automatic mode picked for me, until a shoot photographing a friend's kid on a swing came back with every frame either frozen in a way that looked stiff and lifeless, or blurred in a way that looked like a mistake rather than a choice. That shoot is what pushed me to actually think through shutter speed deliberately instead of letting the camera decide for me.
For a person walking at a normal pace, 1/250 reliably freezes them sharp. For a person running, or a kid on a swing at the peak of its arc, I move to 1/500 or faster. For genuinely fast subjects, a car passing close to the camera, a bird taking off, I go to 1/1000 or higher. These aren't universal rules, they're the starting points I've settled on through trial and error with my own gear, and I adjust from there based on the actual result on screen.
The swing shoot taught me this directly. A perfectly frozen frame of a kid mid-swing, with zero motion blur anywhere in the image, looked oddly static, almost like a posed photo rather than a candid moment. Introducing a small amount of blur specifically in the fastest-moving element, the legs at the bottom of the arc, where speed is highest, while keeping the face reasonably sharp, told a much better story of actual movement. I got there by deliberately shooting the same swing pass at several different shutter speeds and comparing results afterward.
For a subject moving steadily across the frame, a cyclist, a car, panning the camera to track them while using a slower shutter speed, somewhere around 1/30 to 1/60, keeps the subject relatively sharp while blurring the background into streaks that convey speed. My first attempts were mostly failures, with the subject itself blurred from imperfect tracking. It took maybe thirty practice attempts on cyclists at a local park before I consistently kept the subject sharp enough to use.
Freezing fast motion requires a fast shutter speed, which lets in less light, which usually means opening the aperture wider or raising ISO to compensate. On an overcast day trying to freeze the swing shoot, I had to push ISO higher than I'd have liked to maintain 1/500, introducing more grain than a brighter day would have required. This tradeoff is unavoidable and worth planning for before a shoot involving fast subjects, especially in indoor or overcast light where you don't have surplus light to spend on a fast shutter speed.
Video generally follows a different rule of thumb, a shutter speed roughly double your frame rate, so 1/60 for 30fps footage, produces motion that looks natural to the eye rather than either too sharp and stuttery or too smeared. I mention this because it trips up photographers moving into video for the first time, expecting the same fast-shutter instincts from stills to apply, and instead getting footage that looks unnaturally choppy.
Adding flash into the equation changes things again, since flash duration is typically far shorter than any shutter speed you'd set manually, meaning the flash itself effectively freezes motion regardless of your shutter setting, while the shutter speed instead controls how much ambient light fills in around the flash-lit subject. Shooting a first dance with flash, I've deliberately used a slower shutter, around 1/30, specifically to let string lights and ambient venue lighting register in the background while the flash freezes the couple sharply, a combination that a purely stills-focused approach to shutter speed doesn't prepare you for.
Rather than only learning shutter speed choices during client work, where a wrong guess costs a real shot, I've taken to running short personal drills, photographing my own dog running across a yard, or cars passing on a nearby street, purely to test how a specific shutter speed renders a specific type of motion. Reviewing these test shots afterward, side by side at different speeds, has built a much faster intuition than trying to work it out under pressure during a paid session, and it's a habit I'd recommend to anyone still guessing at shutter speed rather than choosing it with intent.
Before any shoot involving movement, I ask what story the motion is telling. A frozen sports moment usually wants genuine sharpness throughout. A moment about energy or speed, the swing, a dancer, a running dog, often benefits from a small amount of intentional blur somewhere in the frame. I no longer default to the fastest shutter speed available just because I can. I pick the speed that matches what the photo is actually about, and I've started shooting a quick range of speeds on any important moving subject specifically so I have options to choose from afterward rather than committing to one guess in the moment.