In a "standard" right-oriented coordinate system, x+ is right, y+ is up, and z+ is towards you. Right-oriented means that if you walk from X+ to Y+ to Z+, you will move counter-clockwards. This is the normal mathematical coordinate system, but as you can see, your suggested coordinate system is also right-oriented (a rotated version of the standard). Usually 3D engines use the standard, but then again it doesn't really matter since you can simply rotate the camera and voila!, things move like your coordinate system.
By "direction zero", I'm guessing you're asking which way the default view is oriented if you feed a 3D engine (0,0,0) as rotation values. This I do not know, but if you're looking at the above-mentioned coordinate system, you're looking into Z-.
Rotations (pitch,yaw,roll) would then be defined as follows: pitch = rotation around X, yaw (heading) = rotation around Y, and roll = rotation around Z. Positive rotation would be defined as counter-clockwise movement if you saw it from the positive side of the axis. But as I said, rotation "zero" is just a matter of definition, so I guess it depends on the 3D engine.
