A friend who is interested in watching her first Indian film asked me for recommendations. She prefers emotional dramas, rather than comedy. Her favorite movies include Cinema Paradiso, The Notebook, Casablanca, It's a Wonderful Life, Grapes of Wrath, Brooklyn, and Call Me By Your Name. After I answered her query, I thought it would be useful to preserve my recommendations in a blog post in case I need them again.
There are very few Indian films that I would class as pure comedy; they really enjoy mixing a bit of comedy into their dramas and their comedies nearly always involve more than a little drama. The full expression of this mix of emotions is the masala (mix!) genre, which combines, comedy, romance, violence, revenge, etc. See wikipedia for more on masala films. They are an acquired taste, but I have certainly acquired it!
Here are movies I have enjoyed in various genres:
crime drama: Andhadhun very modern Indian style dark comedy/crime drama. Minimal music, but it's gorgeous.
horror: Stree Indian horror is not as gruesome as Hollywood horror, which I tend to avoid. Another Rajkummar Rao starring role. He's always good.
drama with music: Gully Boy hip hop in India? Yes, indeed. This was their Oscar entry the year it came out. The leads are top stars, and their movies are almost always worth seeking out. Ditto anything by the director, Zoya Akhtar, who is fabulous. Her Zindagi Na Milegi Dobara is a favorite of mine.
drama with minimal music: There are two sports films that are standouts.Chak De India - Think League of Their Own, with a women's field hockey team. The male lead is the biggest movie star in the world, Shah Rukh Khan. Sudani from Nigeria lovely South Indian sports drama film about an African soccer player stranded in a small village in Karala.
Masala favorites: Om Shanti Om (comedy, mayhem, romance, revenge), Chennai Express (comedy, fight scenes, romance, music), Eega (romance interrupted by murder, incarnation, revenge) Fantastic director, S.S. Rajamouli. His two part fantasy epic, Bahubaali, is totally entertaining. Long, but worth it.
Romantic comedies for people who don't like romantic comedies: Aiyyaa (female centered, very sexy), Mirzya (historical fantasy romance), Qarib Qarib Singlle (the late Irfaan Khan. Such a wonderful actor!!), Ek Ladki Ko Dekha Toh Aisa Laga (a twist on the usual Indian romantic plot, with great cast.)
Indescribable: Ludo (anthology dark comedy crime film), Super Deluxe (black comedy-drama film with elements of science fiction and fantasy)
Note that while most these are "Bollywood" -- Hindi language, produced in Mumbai -- a few are from other parts of India. This what makes Indian film so fascinating to me. There is huge variety even within the Hindi films, and when you step outside that universe, there is even more.