There are two coats on Saks website that seem to fall under the "classic" category, although I think the longer one (40") is the most classic and popular design.
There are so many variations of the Burberry trench, but I have no idea what the name of the most classic one would be. IMO it would be double-breasted, beige, belted, have the signature lining and a back vent.
Have you been the Burberry webiste? It's amazing!
I have the Ivybridge in beige and its the perfect 3-season classic trench