You're close, but not quite there. In Av you set the aperture, ISO, exposure compensation and the camera selects the shutter speed to get a proper exposure for that amount of light - not to stop motion blur. The camera doesnt know how fast your subject is moving so it cant set the shutter to stop it, plus there will be many situations where there is not enough light using the settings you've entered to get a proper exposure AND stop movement.
But, Av is what I use 90% of the time - its kind of a jack-of-all trades setting. Im a landscape shooter so Ill generally set the aperture for the depth of field I want and ISO 100, then let the camera pick my shutter speed. From there, Ill either bracket my shots or use EC to adjust.
In general, Im doing some type of photography where I want control over my DOF for creative purposes - landscapes, wildlife, portraits. Using Av allows me to set what I want and let the camera do the rest - making corrections with EC/ISO as needed.
I dabble using manual sometimes, but I just dont have the "eye" to judge what my shutter speed needs to be but Im practicing by taking my first couple test shots in Av and setting my shutter/aperture in manual based on the best looking image from my test shots. The benefit of this is that once you judge your light, you can set the camera once and get a consistent exposure every time you trip the shutter.
I dont really ever use Tv or P so I wont speak to those.