I'm not sure if there is a checklist or algorithm, but here are some givens when working with flash:

• Shutter speed is not the tool you use for stopping motion. Flash duration is. And, flash duration is normally so brief as to be faster than your fastest shutter speed.
• Longer exposures will allow ambient light to be more of a factor in your exposure. Shooting at maximum sync speed will reduce the effect of ambient lighting (or, in some cases render it insignificant).
• You still use aperture to influence depth of field.
• Distance to the subject is now a factor. Your flash's power decrease inversely to the square of the distance to the subject. With the sun, that's not a big deal because a couple of steps this way or that don't move a subject much in relation to distance to the light source. With a flash, which is both closer and less powerful, a step or two can make quite a difference.
• Distance to the background is now a factor. You can use this to your advantage -- If you want the background de-emphasized, just have the subject closer to you and increase the shutter speed to reduce ambient light effect. That will give you a dark background.
• Ideally, you have an exposure you think suits your subject -- say f/5.6 at 1/200 sec. You set your camera on manual, your flash on TTL and it should "figure out" how much light to emit. Don't go overboard on this because shooting a subject at some distance, f/22, 1/200 sec may be more than your flash can handle.

Since you are supplying your own light, you don't really need the camera picking aperture or shutter speed. You can do this (within reason and sync speed). That means, you are better off using manual mode than Av or Tv. Clearly, the exception to this is if you are using the flash to fill a naturally-lit scene; in that case your original decision tree applies.

As an aside, if you are shooting with the flash on-camera, you are using it in about as limited a way as you can. Anything that will take the flash off the camera will improve things immensely.