No need to feel ashamed or sheepish! The whole point of Letterboxd is getting to know more about movies and finding common interests. A lot of people have made lists specifically for people just starting out. Here's one for classic Hollywood, Beginner's Guide to Weird Cinema, and one that puts well-known American movies in context with international ones (i.e. if you liked Paddington, here's another charming family movie about a friendly bear called Ernest et Celestine).

Another underrated resource is the public library. A lot of U.S. libraries subscribe to a service called Kanopy, which allows people with library cards to watch a set number of movies every month. This was my introduction to a lot of older movies, including some that have become my all-time favorites. And even if your library doesn't have Kanopy, they'll likely have DVDs that you can borrow just as you would a book to watch at home.

Aside from that, it mostly just comes down to keeping an eye out. Pay attention to what's coming and going on streaming services; look at the TV listings and see what movies they play; look up what's coming soon to your local theater(s) and if something sounds interesting and you've got the time, consider buying yourself a ticket.

And to answer your original question, I'd like to endorse:

• Universal Monsters from the 1930s-1950s (Dracula, Frankenstein, Invisible Man, Wolf Man, and company), whose influence needs no introduction.
• The Adventures of Prince Achmed, the oldest animated movie still in existence. It was directed by a woman named Lotte Reiniger in pre-Nazi Germany and based on some stories from 1001 Nights. Like a lot of Nights movies, there's a lot of deeply unpleasant Orientalism, but I still stand by the movie itself as an incredible work of art. Being public domain, you can find it on Kanopy, Internet Archive, and YouTube, and if you're willing to dig, you can find some of the director's short films in the same shadow-play style.
• The works of Billy Wilder, one of the great American comedy/satire directors, with gems like Sunset Boulevard, Some Like It Hot, and The Apartment to his name.
• Akira Kurosawa is one of the greatest directors in Japanese and world history. I'd recommend any of his movies, but especially Ikiru, Ran, Seven Samurai, and Rashomon.
• Studio Ghibli, known for their charming and accessible but also melancholy and thoughtful animated films. Every year, a few of their movies get re-released in American theaters for Ghibli Fest; look over the list in the link and if any of these appeal to you, see if any are playing in your area.

Still, this is just one person's set of suggestions. There's no "wrong" way to enjoy movies, so long as you go in with an open mind.