You live in a nice,warm, bright climate area of the US. You have the luxury of being able to shoot at 1/500 second much of the year. The slightly faster shutter speeds, like 1/350 to 1/500, really do help stop subject motion blur, camera shake, camera vibration, and so on. If you look really closely at things in motion in your photos, you might see small amounts of subject motion at speeds like 1/125 second. When you really zoom in on an image shot at 1/125 second, there can easily be slight blurring...
So, basically try and shoot at the higher speeds. Another thing you will find out soon is that your sensor might get dust on it, and the smaller lens apertures like f/11, will show every spec of dust on your sensor as a black dark dot on your skies and even-toned light areas. Shooting at the beach at f/16 to f/22 is an exercise in "pepper sprinkled skies" with a dirty sensor. With a brand new camera, you have about six months, maybe a year until the sensor gets so dirty you're going bonkers when you shoot sky scenes.
Easy way to learn is to shoot in P, the Shiftable Program. The camera will pick the right aperture/shutter combo; with a Nikon,just use the thumb wheel to try alternate equivalent exposures. Slow exposures when panning the camera while photographing people driving by on motorcycles, like 1/8 or 1/15 second; fast speeds like 1/500 or faster when shooting seagulls diving for baitfish scraps a fisherman tosses off the pier.