Whenever I move my mouse, the window where the mouse is gets the focus. That's the only true way of a good windowing system!
Only the default theme takes like 0.5 to 1 second to switch between windows. I can see some animations with the stupid shadow and colors changing. Is there a way to suppress that animation and even the shadow?
I'm thinking that maybe I need to try other themes to resolve the issue. In that case, do you know of a theme which would not have those bells and whistles?
Install the took "GNOME Tweaks" from the Ubuntu Software Center. On the first tab, there is an option to disable animations.
The shadow is defined by the theme, and is rendered if compositing is active. A.f.a.i.k., you cannot disable compositing in Gnome Shell.
Slow or faster animations typically will not depend on the theme. Slow and sluggish animations may be due to issues with the graphical card and driver.
b.t.w., GNOME Tweaks will also allow you to set the Windows focus mode. I would not agree with your statement "Whenever I move my mouse, the window where the mouse is gets the focus. That's the only true way of a good windowing system!". As a heavy keyboard user, I would not like that my mouse would be controlling which window is active. In other words, this is a subjective statement.
You may want to explore other, much more out-of-the-box customizable desktop environments like xfce (Xubuntu) or Mate (Ubuntu Mate).