How do I change my default session?

On Debian, you should set the x-session-manager default command to choose your default session manager:

# update-alternatives --config x-session-manager

There, you can select the session manager you want GDM3 to use by default.

If gnome-session-classic does not appear in the listing, try creating the link on your own. Something like the following:

# update-alternatives --install /usr/bin/x-session-manager x-session-manager /usr/bin/gnome-session-classic 60

Then you should be able to select gnome-classic with update-alternatives --config x-session-manager.

To customize the session managers listed by GDM, I think the only way is to go to /usr/share/xsessions and create/remove Desktop Entry files there. The format is easy to understand, but in case you need help, you can consult the Desktop Entry specification or the GNOME documentation about Desktop Entry files.

With GDM, have you tried modifying your ~/.dmrc file? You can set gnome classic as your default session like this:

[Desktop]
Session=gnome-classic

reference: GDM manual