Best newspaper is USA Today. A comedy professional's goldmine. It gives you news you don't have to think about. The major aspect of humor is to provide a humorous comment about a universally recognized person, place, or event or shared experience. And note, what we carry around in our head is usually just a snapshot of two or three facts per joke topic.
For instance, to get your biggest laughs with a Hillary Clinton joke - you focus on the fact that she is very cold/tough (Letterman - right after his heart attack, "I have a lot more sympathy now for the president. I was with Hillary just a half hour and look what happened to me.") and New York carpet bagger (Leno: President Clinton is off to India and Pakistan for two weeks, which is one week more than Hillary has lived in New York.").
You very likely will not get laughs focusing on these other true facts about Hillary: She's from Chicago, mother of a college student, worked on the Nixon impeachment team, a lawyer, she was the leading proponent for Universal Health coverage .... These facts are not in people's everyday consciousness.
Bill Clinton - Rascally skirt chaser with a taste for unattractive women. (No examples needed. Think of a Bill Clinton and/or Monica Lewinsky sex joke....) You don't hear jokes about him being a Rhodes scholar, a draft dodger, not inhaling, or the fact that Alabama sued to have him disbarred. These facts are not in people's everyday consciousness.
Jokes work on immediate-in-the-mind references - that's what you get from USA Today. It is a humor professional's dream. Its news stories are essentially joke concepts and/or setups. They give you the most common denominator facts and all you have to do is write the punch line(s).
People Magazine. Same usefulness. Tells you who's in the news and doesn't muddle the waters with in-depth analysis. Just the most common traits. Be careful, though. Not everybody in People is worth a joke. To fill content they sometimes run stories about people who are only getting their 15 minutes of fame. Could work for a casual conversation joke, but avoid putting it in a speech you expect to give for a while.
And also, these two sources are great for a bit that is somewhat old. Let's imagine you have a chunk, nine years old about going on your first airline trip. USA Today might do a story on airline safety, The Federal Aviation Administration, airline food, flight attendants, an impeding airline employee strike, etc. For any of these you simply say, "Did you read in USA Today about "(quote headline)?" and segue into your now "topical" bit. Great way to give new life to old bits.