Jack Benny's characterization is one of the greats. He's vain and cheap. Both are qualities we all have and we laugh at Benny recognizing our own foibles. Benny (and his well paid writers as Benny was actually a generous man) mined these personality faults for decades.
Chaplin's "Little Tramp" -- perhaps the most recognizable comic character in history -- gives us insight into character. He's poor and a vagabond. Yet "The Little Fellow" (as Chaplin referred to the character) dresses in a bowler, a walking stick, ill-fitting clothes but those of the higher class. Chaplin's movement and manner affect those of the wealthy.
So his characterization and costume is in direct contradiction to what we know to be true -- that he's a penniless tramp.
Note that these faults could be played dramatically. Someone excessively frugal could be a Scrouge. All comic characterizations should have a dramatic spine -- something for the audience to form a human connection. We laugh at these faults recognizing them in people we know and perhaps ourselves.
To form comic characters begin with a list of faults. Exaggerate these faults. Felix from THE ODD COUPLE is not slightly neat; he's obsessive compulsive. Likewise, Oscar is not the average slob; he's the extreme. Neil Simon tossed the two characters together creating comic conflict. Then repeated this formula for a very profitable writing career. Much to learn from following this successful formula.
Having these great characters allows the writer to let the comedy flow from character. The effectiveness of jokes is multiplied and the audience appreciates it more.
For example, with Benny's famous "Your money or your life!" line (google it if you're not familiar as it was the longest laugh in radio history). The audience laughs BEFORE the punch line in anticipation. The character Benny created was so strong the audience recognized the great set up and situation. True dilemma for Benny -- his money or his life?
So having that depth of comic characterization lets joke after joke be created. Contrast this with stand alone gags. The POLICE SQUAD television series lasted only six episodes. This was in part of the comedy style requiring the audience's attention (ZAZ's explanation). But mostly as there was a lack of real character depth. All math.
Contrast that show with GET SMART (pilot by Brooks and Buck Henry), which had wonderful characters. The audience loved the characters, especially Don Adams' wonderful Maxwell Smart, and the show -- with just as many crazy gags -- last for years. Also, it's more enjoyable to watch again and again because of the characters.
How do we win the heart of an audience? Chaplin's formula was "close-up for drama" and "wide shot for comedy." Why? In the end of CITY LIGHTS Chaplin is at his most effective drawing audience empathy. In close up we are drawn into the drama of the situation and we feel for the Tramp as the blind girl he has help find sight recognizes him.
By contrast, the wide shot for comedy keeps the audience at a distance. No matter how bad the prat fall in comedy it doesn't really hurt. There's a distance, and one could argue sadistic tendency, for the audience to laugh. The full shot lets the audience stand back from the situation and laugh.
To sum up, when creating your comic characters find their faults. Take these faults to the extreme. Put the characters in direct conflict with each other and let the sparks fly. All these are the tools of the dramatist as well. The comic writer must do everything the dramatist does and make it funny.
Go to it!