I have tweaked my mouse sensitivity to be just right, and swapped the mouse buttons since I use it left-handed. This was done using the user "Mouse & Touchpad" settings in Gnome.
I'd like this to apply to the login screen and all other user sessions (since they're all mine as well anyway). I'm using Gnome 3.8 under 13.10, but other sessions might use Unity or XFCE.
How do I apply my session mouse settings globally?
There's no central place to apply mouse settings globally.
Why?
let's review how a user session starts in a X window environment(GNOME, KDE, XFCE,etc.).
a display manager starts X server which read its configuration file xorg.conf and shows a login window (typically created by an independent greeter program). so the only way to change mouse settings at the moment is through xorg.conf.
after you login, a session manager starts a settings daemon which re-applies the settings it stored, which can overwrite those settings in xorg.conf. for different desktop environment, the settings daemons are different and they have no responsiblity to respect each other's settings. normaly, there's a GUI frontend for each settings daemon.
a clarification on the settings daemon. in GNOME, it's gnome-settings-daemon while in XFCE it's xfsettingsd. In Unity it's gnome-settings-daemon because Ubuntu reuses most of the GNOME stack.
Back to your requirements.
apply to the login screen
the only way to achieve this is through xorg.conf. because the settings-daemon is not started at the time.
to change the mouse to be left handed, refer to how can I configure a specific usb mouse model as left-handed?
to change the mouse acceleration, refer to https://wiki.archlinux.org/index.php/Mouse_acceleration
apply to all other user sessions
this is simple. all desktop environment have settings programs. change the mouse settings of every desktop environment to your desired value.