How can I automate window arrangement? I know and have been reading a few ideas about how to "import" the features of xmonad/tiling window managers in OSX. I don't care much about the X11/Xquartz windows, but about conventional OSX windows.

Now, all the solutions I have seen around lack the one feature I'd really like to have: not to worry about windows anymore.

Let me explain:

I'd like to have a system (as in xmonad on linux) in which I have 2/3 different modes (in xmonad I'd use Simplest, TwoPanes and Grid) and windows (newly created or existing) automagically adhere to the layout I have selected: no mouse involved, no keys to be pressed. Then I'd need a keyboard shortcut to be able to switch from one mode to another.

Obviously a big plus would be to be able to handle exceptions (as in xmonad, floating windows) or a keyboard shortcut to move around a window freely.
Try out Stay. It lets you save window configurations (position and size) in profiles. Unfortunately, these profiles only deal (multi) display arrangements.