Agree about Beethoven's 5th.
Listen to the first movement. Those familiar with Classical scoff at it as all-too-familiar, but it is a perfect piece of music. Find a good performance. There are so many: Bernstein, Giulini, Osawa, Von Karajan to name a few. If you listen to the first movement (about 8 minutes, or so) and find yourself unmoved, then you will never be a fan of Classical music. I think it's better to learn that from the outset than to torture yourself plodding through yet another Bach concerto.
If you like the first movement of the 5th, listen to the second and third and fourth movements. Then listen to the fourth movement of Beethoven's ninth. Still with us? Try the whole ninth. From there, the world of Classical is wide open to you.