I started using AIGLX and compiz today.
No, that's not my computer.

It appears that to get the window manager actions to use the Windows button (a.k.a. Mod4 a.k.a. Super) insteaed of Alt, you need to open up gconf-editor and go into /apps/compiz and change various settings in there.

I found that the mouse binding for moving a window (by clicking anywhere inside it) would revert to <Alt>Button1 every time I logged in. I found some forum posts online which point at freedesktop bug 8085. To work around it, I created a shell script which looks like this:

#!/bin/sh
gconftool-2 -t string -s /apps/compiz/plugins/move/allscreens/options/initiate_button '<Mod4>Button1'
gconftool-2 -t string -s /apps/compiz/plugins/resize/allscreens/options/initiate_button 'Disabled'
gconftool-2 -t int -s /apps/compiz/general/screen0/options/size 3 

I added the second line because compiz appears to freeze on my machine if I resize a window using that binding.

I'll add to the script as I discover other settings getting reverted.