But how do I automate that so Compiz starts every time I log in?
Hi. I am not familiar with compiz, but here are some ideas.
So you can create .desktop file that will be launched automatically when you login.
System-wide location is /etc/xdg/autostart, but I prefer local:
Here is how you can launch xcalc on each login:
$ cat ~/.config/autostart/xcalc.desktop
[Desktop Entry]
Type=Application
Exec=xcalc
Try to do the same with compiz --replace.
Chances are high that you already have this file in "/usr/share/applications/compiz-start.desktop", so you can simply copy or link (ln -s) it.
Another approach is to install it as an alternative for x-window-manager, but this hasn't been done by package maintainer, so there should be some reasons not to do that..