I am far from common but I shall answer your question anyway.

The answer depends on what you want to do. If it's to honor film as a medium and inaugerate it with the best films available on DVD, then I'd say go the classic route with
Gone With the Wind or
Citizen Kane or
Casablanca; something with the smell of pop corn and a sense of movie majesty in it.
Of course...
that's not what most people do..... they pick the loudest, most sensational, most eye-opening DVD in their collection. In that sense something like
Lord of the Rings: The Fellowship of the Ring EE is perfect because it'll feed your jones and give you a sense of movie history. The best part is you can just keep going after that with
Lord of the Rings: The Two Towers EE. Seeing as
Star Wars: A New Hope isn't available, this is the next best thing.
P.S.- If you have to limit your viewing to just what you have in your current collection (a shame not to get something new just for the occasion :p)) then definitely
Toy Story and
Toy Story 2. They are outstanding DVDs for both the ear and the eye.