If there is enough light, Av mode is good coz it gives a consistent DOF across all pics. If it gets too dark, the shutter speed drops, and you risk getting the movement streaking effect in your pics. Have to keep an eye on the shutter speed at all times when using this mode.
Tv gives a "guaranteed" hand-holdability, but again, when the light falls, the camera just underexposes, and you'd have to trust the flash to meter the main subject correctly. Even when there is enough light, the aperture can vary quite a bit when the lighting changes, so the amount of background can vary a lot between the pics.
Manual gives a consistent DOF across the set and ensures a shutter speed that is high enough. If the flash system is recharging fast enough and metering is consistent, the results are consistent. However, the exposure can get thrown by reflective surfaces and underexpose. Also, if the lighting suddenly increases to more than 2 stops above the manual (fixed) setting, every shot will be badly overexposed. This can happen easily on say, a sudden strong spotlight on an individual with a dark curtain background.
There's no single correct answer. Have to understand how camera and flash metering works, and how to adapt to changing lighting.