Its actually a great measure. This allows you to enforce stricter policies, you can put this "secure terminal" behind a locked door requiring a access card, and you can lock down this terminal very well.
But you need to improve it a little bit. I would not suggest using GMAIL because that would allow a rogue user to compromise material. A user could easily insert illicit software by sending a mail from himself to the "secure terminal GMAIL adress", and the user can easily leak confidental material by using GMAIL to mail himself.
If the GMAIL adress leaks out, rogue users on the outside could send virus to the adress and compromise the terminal.
I would instead set up some own secure system for importing and exporting material from the computer. This system can then be restricted in ways to prevent leaking of information, for example mandatory encryption or restricted to a set of import or export email adresses. This solution should preferable be hosted locally, so the access to the service can be tightly controlled and be limited to the secure terminal only.
I would also suggest using a secure browser based system, like WebConverger, to prevent compromise. WebConverger is OpenSource and can easily be modified in the boot API to allow booting into secure local websites, without having to use the config service. WebConverger is actually made with public terminals in mind, so the system is protected against local compromise aswell, so even if a rogue user infront of terminal tries to compromise it, it will stand against it.
Instead of using Libreoffice, I would suggest using a web-based office system, preferable hosted locally, that is loaded inside the WebConverger.
And needless to say, block all traffic to all sites except for permitted ones.
I would suggest not using a proxy for this, instead, use a firewall, and filter by IP-adress instead, by permitting all good sites and then finishing with a "BLOCK ALL".
Preferable, its a good idea to use the hosts file to code all the good sites, and then set the DNS IP to 127.0.0.1
Then you can block all DNS traffic, so no "tunneling" of traffic can be done.
But one thing I would suggest:
Use a secure USB memory that do have a write-protect switch, like Kanguru FlashTrust:
On this memory, you store the operating system, in the form of a "live operating system", that permit no modifications to be stored between boots.
After initial configuration is done, the memory is simply locked with the write-protect switch.
The whole computer, must then be put into a lockable enclosure or secure location, such as the actual computer is not physically accessible by the end users. This prevents all usage of end user USB memories and such. This can be accomplished either by simply using a anti-theft-cage that does not permit access to the computer's IO ports once the enclosure is locked, or you can tuck away the computer in a server room and use a KVM-over-Ethernet solution to place a secure display, keyboard and mouse in the secure room.
Another security measure I would suggest, is that you wire up the access system (many access control systems today have additional IO relays that can be used to control equipment), so the following rules are used:
1: The door have a door sensor, like a magnetic contact or lock sensor, that can detect if the door is open or closed.
2: When someone swipes their card at the ENTRY terminal, the door will open. When the door closes successfully (with the user inside), the power to the terminal will be given by the relay. This can be accomplished by simply using a low-voltage computer system like INTEL NUC, and then using the relay to switch on and off the low voltage side of the transformer.
3: The power LED of the computer, is wired to the access control's "BUSY" input, which will disallow entry to the room while the computer is on.
4: After a set period of inactivity, like 10 minutes, the computer will shut off itself (halt) and this will clear the "BUSY" signal, allowing access to the room again, for example if a user accidentially closes the door without entering.
5: When a user swipes the card at the EXIT terminal, the system will power off the system automatically by just cutting power, and then unlock door.
The good thing with this, is that the terminal will be guranteed clean when a user enters the room, no matter what the previous or a rogue user installed or compromised or did whatever to the terminal, any such tampering will be gone.
No logon system or authentication system is needed on the computer. All authentication is physically handled by the access control system, which can also be hooked up to a alarm panel to prevent any attempt of "hacking" the secure computer. If you want some sort of access control to different sets of information depending on which user is on computer, then most access control panels do have a API where you can check whoever is inside the room (user which swiped at ENTRY latest but not yet at EXIT), and thus use that for access control.
By doing this, you will prevent most forms of compromise. Its better to use technical solutions to prevent the user from violating the policies instead of having policies.
And a last thing: Drop the wifi. Even if a wifi can be made secure with encryption and VPN's, you gain much more control if you use physical cables, like you gain much more control with physical locks.