In view of the way the discussion has gone, start with a shorter, early one. I think The looking Glass War is great - full of atmosphere from the first page.
Good choice. 'The Spy Who Came in from the Cold' would be another.
Am currently reading the more recent Le Carrés and have just finished this:
While they don't equal the earlier classics, they still stand out nowadays as exemplary writing. Of these newer ones, the best I've come across so far is this, but I haven't got to the end of the list yet!