Do you have a particular reason for using Linux Mint and/or Cinnamon WM?
You could create a new user, set their WM to openbox, i3 or another WM that is configurable from a textfile and remove functionality that way.
Alternatively, you could just set ~/.xinitrc to
exec firefox which works but isn't the best solution IMO.
You should also take into account who will access this machine. Normal users, not much is needed to lock it down. If you don't want Linux users altering the system, then disable VTs, disable sshd and other unnecessary services.
You may opt to instead use GRUB2 to boot a Linux LiveCD ISO from the harddrive for guests. Using this technique you could boot something like JustBrowsing LiveCD (disclaimer: personal plug)