[Disclaimer: some of this post was written while under the fog of Percoset prescribed to me due to a massive kidney stone shortly before publishing. However, I made a commitment to have this thing up and ready, so here it is. It isn't anywhere near perfect or what I was hoping for, and I'm sure you'll be able to tell where/when the pain and drugs--and a little procrastination--got to be too much. Either way, I hope you take a little enjoyment from this. --Peter]
Getting into classic movies when you haven't really watched them before doesn't have to be a difficult prospect. You already know your own taste, so you can take it from there to decide where you want to start. But if you're looking for my advice...The Americanization of Emily (1964) is a good gateway to old movies (although I wouldn't call this movie old, per se).
It has humor; love and sex (well, 1964 sex); it has drama in the form of anti-war sentiment; an absolutely incredible cast--James Garner, Julie Andrews, Melvyn Douglas, and James Coburn; and Mary Poppins herself gets called a bitch! Are you intrigued yet? Read on.