There isn't any clear "better" exposure mode when using flash.... It's just different.
Simply remember FILL versus FULL.
When using the camera in any of the auto exposure modes (Av, Tv, P) with flash, the camera will set the exposure according to the ambient light condition (as if the flash weren't there) and then fire the flash as FILL. The output of the flash is held back or reduced about 1.5 or 1.7 stops, unless you adjust it more or less.
This FILL flash firing automatically is just enough to open up shadows, add a catchlight, etc. It will not stop subject movement... Instead with movement it can cause ghosting, as the camera is still relying primarily upon ambient light for the exposure.
Switch to M or Manual if you want FULL flash, where the flash is the main light source. Use this to stop action. Or to be able to use a faster shutter speed that helps prevent camera shake blur. Above a certain point (where it stops recording a lot of ambient light), the shutter speed actually isn't too important. That's because the short duration of the flash itself acts like a shutter speed as fast as 1/720 in many cases, even higher with some special flashes. The flash essentially "becomes" your shutter and you control the distance the flash reaches by changing the aperture and/or ISO. (Unless you choose to manually adjust everything so that the ambient light is still recorded.)
You could have used higher ISO and gotten faster shutter speeds.
Often you can use the camera set to Av or Tv or P as a starting point, noting what it sets, then switch to M and set things manually, reducing how much ambient lit background is captured in the image, for example.
No matter what exposure mode you have set on the camera, you can use Flash Exposure Compensation to either increase or decrease the exposure from the flash. Of course, this will only effect the FILL portion of the exposure, when using any of the camera's auto exposure modes.
The flash will usually recycle much faster when used as FILL, than it will when used as FULL flash.