I am not a huge Chaplin fan since I have always been more of a Buster Keaton fan myself. But I know a bit about Chaplin. My favorite film of his is "The Kid" it has the normal slapstick in it but the end will bring you to tears, it was one of the first if not the first film to be able to incorarate high drama and comedy and still work. The Great Dictator is a good choice as well, it is the first the the "Tramp" speaks, and what he says is relevent even today in his speach at the end, if not a little wishful. Of couse since he used the term "Comrade" everyone thought that Chaplin was red and it was the begining of the end for him in the U.S.A.. I am not to big of a fan of "Modern Times", although last year I wrote a report about the breakfast macine used in the film which is really great but the film has some problems. "The Gold Rush" is an earlier Chaplin film to take a look at that is really great. You will find that a lot of sight gags that are very familar to us today and even trendy to the point of being unusable today are in these films but you have to remember that these are things that were never seen when the films were made.
Chaplin was amazing though he would direct write produce act edit and sometimes even write the music, and yes silent films had music that would be put onto sheet music for the band or the piano player to play along to the film. To do all these things was not rare in the early days of cinema but Chaplin was making films in a much the same was as we do today which is much more complex then what even D.W. Giffith was doing. People like to downplay Chaplin's contabution to the cinema of today but without him movies may have been very different. He made a movie into a narritive not just a series of events.
I suggest that if you want to check out Chaplin then you should check out Buster Keaton as well. A good place to start with him is "Sherlock Jr." and "Steamboat Bill" which is the film that Walt Disney used for inspertation for Steamboat Willie. Keaton did not really have films that had the kind of depth that Chaplin was known for but he is far more entertaining to watch. He was the Jackie Chan of his day doing huge stunts from riding on the fronts of movieng trains to sets fall on him to falling 2 or 3 stories all without ever changing the expresion on his face. And he was a snapy dresser too!
Although "Modern Times" and "The Great Dictator" have diolog and music to a degree since they we produced into the talkie era when it comes to looking for silent films on DVD or VHS you have to be carefull to get a version of the film that has a score that was written for the film when it first came out, if you see a silent film with the wrong music it can really change the feel of the film. You will also find that you will hear dialog in your head which can be kind of strange. If the music is wrong then you might get the wrong idea about what the film is trying to say to you as the viewer. Good Luck!
