Use shutter priority when it is important to control exposure time (i.e. you need to freeze something or want to blur something).
Use aperture priority when you need to fix depth of field or must to stop the lens down for another good technical reason like quality.
Use manual when the scene in front of you might confuse the camera metering, or it needs to be over-ridden for another reason like using flash.
That's it really. You can use exposure compensation to help overall, or if your camera has it, spot metering to manage the exposure automatically but with less general metering.