Okay, so here's what I find the practical difference between Aperture priority and Shutter priority to be.
I use aperture priority by default, and adjust the setting based on how much of the scene I want to be in focus versus how much should be blurry. If I want to make a person stand out sharp against a blurry background, I use a very low f/stop (aperture) value..like f/4 or less if you can. If I want everything to be in sharp focus, or shooting buildings, I'll use f/11 or f/16. If you have a lens that does f/1.4 or f/2.8, you may literally have to pick a point on someone's face to be in focus, as everything else will be blurry - like do you want the eyebrow or the eye or the tip of the nose. I don't mess around with in-betweens. Either wide-open, f/8, f/11, or as small as possible depending on the lens (you probably have an f/22 I think).
The only three uses I have for shutter priority are as follows, but I'm a simple guy.
1) Stop-motion. Hot babe in the surf frolicking about, and you want to stop every droplet of water around her. Use a shutter of 1/2000th or faster.
2) Moving water. Creek, stream, river, waterfalls. Turn the water into a soft, foggy milk while the ground around it stays in sharp focus. 1/5th, 1/2nd, 1.3 seconds, or slower.
3) Race cars on-track. Following the car with the center of the door in the crosshairs, holding the shutter release down, making the car appear razor sharp while everything around it seems to be 'moving'. 1/30th to 1/60th.
The camera will figure out aperture to make sure the picture gets properly exposed.
If you want to do a little of both, you have to go into manual mode, where you set the aperture and shutter. You can use one mode or the other to get in the ballpark, or if your viewfinder is like mine, it will tell you if the shot will be over/under exposed based on your settings and available light with a little graph-like readout...probably has a + at one end and a - at the other.
Hope you get those books I recommended soon, because they're a lot better at this than we are.