I will offer you a glimpse of some characters in my favorite Shakespeare comedy, The Taming of the Shrew.
Katherine (Kate) - She doesn't try to be funny or humorous, but she is so overly petulant and shrewish that she becomes comical. What is interesting to study about Kate is her motivation for that behavior and her "transformation" from shrew to obedient wife to, arguably, a full partner in the marriage.
Petruchio - He's so outrageously crude and arrogant, and we find ourselves rooting for him early on. Soon, though, we're laughing at the pain and discomfort he's brought upon himself. In the end, we have hope that he'll be a decent husband and partner to Kate.
Gremio and Hortensio - They are the suitors, and they're often played as Mutt and Jeff (Abbot and Costello, Laurel and Hardy) physical opposites to add to their ridiculousness. Funny guys.
Baptista - Single father to Katherine and younger daughter Bianca. He's a study in fear and intimidation and lack of self-awareness--or any awareness at all, at times.
Bianca - Kate's younger daughter is one of the most intriguing characters to watch or play, since she's playing all kinds of sweetness and light while working furiously behind the scenes to get her own way at every turn.