Lastpass - probably the biggest thing most users can do to improve security, use a secure password manager.
NoScript - another critical security tool
Adblock Plus
BetterPrivacy
WOT - web of trust, gives quick security info on any website
Lazarus - really useful ability to recover input, prevent losing a post
CompactMenu - add menu to the navigation toolbar, hide menu bar
TooManyTabs - great for saving lots of tabs
Places Context Menu - allows bookmarks to be sorted by visit count

Per the post from Clem:

"As I said in the previous chapter, we're "considering" doing that... it's not set in stone yet."

So to be clear, what they are proposing is, LMDE lke Linux Mint would keep the Jesse code base for the next 2+ years, enabling the Mint team to put more effort into improving the desktop experience and user applications. But LMDE would get these improvements on a rolling basis, so LMDE would actually get new software before the Ubuntu based Linux Mint, which would continue to get those updates through point releases.

This is what is being considered, it's not decided yet.

So long as the administrator agrees to whitelist it, and allow the browser add-on, it should work fine. It doesn't require any USB, or separate software to be installed. It doesn't save passwords anywhere locally. Everything is stored encrypted on their server, and unencrypted by the browser add-on. This is both very secure and very convenient.

I'd think this is something most administrators in such environments would allow if asked, since it's going to make their own lives a lot easier.