Into history? – Shoulder Arms. Or (the sort of a sequel) The Great Dictator
Into political/social issues? – Easy Street, The Kid, Modern Times, Monsieur Verdoux, A King in New York
Want a good cry that tears your heart out and rips it to shreds and stomps it on the ground? – The Kid, Limelight
Romantic? – The Immigrant, The Gold Rush, City Lights, The Circus, Limelight
Film Noir? Monsieur Verdoux
Artsy (and that does not star Chaplin but everything else behind the scenes is Chaplin): A Woman of Paris
Afraid of a strictly silent film and want something in-between all-silent and all-talkie? Modern Times
Want a silent film that is narrated? The 1942 version of The Gold Rush. Chaplin narrates it himself. As well as composed the music.
Great music? 1942 version of The Gold Rush, City Lights, Limelight
A general good place to start (and the first one I saw) – Modern Times
But the best environment to watch his films is with a group of people (which, I know, can be tricky with the current pandemic). There is something about watching with an audience that make films more enjoyable, and in this case, funnier. Especially when it comes to silent films. A great YouTuber I enjoy is Austin McConnell. A couple years ago he did a video about his experiences in how he learned to enjoy silent movies.
And ever since the Covid pandemic started, Ben Model has been running weekly live-streams of comedy shorts of not only Chaplin, but other comedians as well, both famous and not so famous. Every Sunday he provides live piano improvised accompaniment. A fun way to watch with a virtual audience and get some trivia about the movies.