The kind of news you want is that which remains relevant tomorrow.
Some news are designed to create cumulative knowledge and cumulative understanding. Search for those formats and make a habit of reading them regularly, but not necessarily daily.
A great example is the economist and in particular its weekly recap.
By the way, I'm not a fan of podcasts because you're not in control when listening. They want you to spend as much time as possible, but you want to skim and skip quickly. Text is vastly superior for that.