How to perfectly align UV coordinates automatically? I have this setup: 

The mesh is only the visible top side, with a mirror modifier for the bottom part.
Now I want to unwrap it like in the picture. I want the inner circle (red) to go to the top of the UV map...

The problem is that no matter what automatic unwrapping I use, it never works as intended. 
The closest I've gotten was by using "follow quads", but that skewed the UV map a lot: 

I used the result from the second image and manually adjusted the vertices with a lot of scaling and "align auto", but its very far from perfect as you can see in the first image.

Here's what I want exactly:


The uv vertices should be distributed evenly (horizontally)
The middle line (yellow) should be on a "natural" y height (so there's no stretching)


I hope it's clear what I want to achieve. I'm sure there must be some automatic way to perfectly align and distribute the UVs in this way.

By the way: If you look closely you can see that I already placed a uv seam (aligned with the green y axis in the screenshot) but that didn't really help.
Follow Active Quads is indeed the best automatic preset to use in this situation, however its use is slightly nuanced, and until recently I didn't know how to properly use it myself.

Start by erasing your existing UV Map from the Properties Window > Object Data > UV Maps, so you can start afresh.

Select one random face, any four sided face will do, and unwrap it using the basic U > Unwrap > Reset option so it is unwraped as a perfect square.

This will also make it the nominal active quad, only then can the Follow Active Quads option be used since it will use the active face's coordinates to unwrap the remaining mesh.

Now select all faces and unwrap them using U Unwrap > Follow Active Quads, should yield an even quad orthogonal grid.

Afterwards if you wish to make it fit inside de [0,1] UV space then either scale it down until if vaguely fits inside the image area, turn on UV > Constrain to Image Bounds and scale it up manually; or use the operator UV > Pack Islands to automatically fit maintaining proportions.