Unfortunately, 'out-of-the-box' Firefox under Linux Mint doesn't show suggestions when you type in search box.
How to fix:
- download Firefox from mozilla.org
- find google.xml in archive (firefox/browser/searchplugins)
- copy this file to local firefox setting directory (in my case it was ~/.mozilla/firefox/mwad0hks.default/searchplugins)
- restart browser
- enable 'Provide search suggestions' box in search settings