Direction of Angle

First off, I understand the gun needs to be angled. What I am not grasping is if the direction the angle is at matters?
For example, do you need to follow a horizontal line horizontally or can you follow it perpendicularly?

If you angle the gun, you're going to miss the target
My understanding is that when you are lining the needle (therefore the machine) needs to be at a near verticle position (this prevents the ink from spreading under the skin and causing blowouts) When colour packing, the needle needs to be at an approximate 45 degree angle so that the ink spreads a little under the skin so more coverage is gained.
This is only my understanding, others may have different opinions.

It depends on what you're aiming to do, as Pete said lining should be close to vertical, packing and shadows will be more with an angle.

See it that way: if you want a crisp, clean line, you'll need a consistent ink flow, a consistent motion, and a consistent speed.
This 3 aspects are meant to keep a good control of the lining.

Ink flow, which is controlling the width of your lines > too much ink = bolder, not enough = weak/grey.

Motion is keeping the same angle (the ink deposit stays at the same depht, at a locked angle, meaning it's not flowing here and there, but exactly under the stencil) and following the stencil path (no woobles).

Speed is controlling ink flow, so a consistent speed throughout all your lining will ensure it is looking the same everywhere.

For gradients and packing, i'll let the more advanced give their explanations.

Peace,

DKJ