Shutter speed & aperture can be considered both from a technical and aesthetic point of view. The "best" mode is the one that gives you the result you want
Some general points: most lenses perform at their best (sharpest, least distortion) at around f8 - f11. With a cheap lens, the difference between f8 and, say f4, can be remarkable. More expensive lenses tend to have a more consistent performance, so this need not be such a consideration. Note that some people are under the impression that if f8 is good, f16 is better. Not so - lens performance tends to drop off a bit beyond f11.
DOF is not a "quality" issue - its an aesthetic one. You decide how far you want the zone of acceptable sharpness to extend behind and in front of the subject.
Shutter speed: you need to make sure you can hold the camera still enough to get a crisp image - Anders' rule of thumb is a good guide, but again, there is an aesthetic element - if you want motion blur, you will have to select a suitable shutter speed to acheive this.
Personally, I tend to shoot TV
mode for moving subjects, AV
mode for static. The reason is mostly aesthetic - I like a bit of motion in my pics (whirling props, motion-blurred background), so on any "action" pic, I will select the slowest shutter speed I think I can handle and let the aperture fall where it may - this is one of the reasons I invested in L lenses ... I know they will produce good results wide open or at f22.
For static stuff, shutter speed doesn't much matter (within reason) so here I will select AV
mode to ensure I have control of my DoF - I may for instance want to shoot from a wingtip and get the whole aircraft sharp, or I may want to put a messy background out of focus.
why do you shoot sometimes around f/14-16?
This would normally be in the case of an action shot - because I've chosen a slow shutter speed to get some motion blur, the aperture will tend to be quite high in decent light.
A note on P mode - while this mode will usually find a balance between shutter and aperture which will ensure a technically good result, basically you're handing creative control over to the camera. For instance, P mode deosn't know you are panning a shot to blur the background, and will probably select a higher shutter speed than you would want to use for the effect.
Colin K. Work, Pixstel