Whatever you want! There's no right or wrong when it comes to podcasts. Thousands of them exist for all kinds of interests from politics and news to comedy and role playing. There are as many podcast categories as there are book categories in a library!
Because there are so many options, it can be useful when getting started to look at popular podcasts in the podcast provider you've chosen.
These links are to several podcast lists to get you started:
Do I have to start at the beginning?
Podcasts are not necessarily serialized and many provide stand alone episodes. Don't feel like you have to start at the beginning of a podcast to decide if you like it or not; frequently podcasters "find their groove" as they gain experience and recent episodes might be more representative of the content they produce than the first ten episodes.
Are there family friendly podcasts?
Yes, there are! But there is no universal rating standard for podcasts the way there is for movies and television, and not all podcasts are appropriate for all audiences. While many podcast providers mark episodes when explicit content is present, that doesn't guarantee every unmarked episode is family friendly. If you are considering sharing a podcast with younger or vulnerable audiences, listen to it yourself first or search for reviews about its content.
Not all podcasters are experts and unfortunately they won't all tell you that. It's important to recognize that podcasts are created with a point of view, especially when listening to political and editorial podcasts.
What if I don't like something recommended to me?
You might not agree with every podcast you hear. You might not think the tone of a true crime podcast is respectful, or may dislike the people who make it. That's okay! You don't have to love every podcast. Take a step back and ask yourself, "Do I enjoy this? Am I the intended audience?"
If you answer no, feel free to move on and try something new.
Who can I ask for recommendations?
Ask your librarian!
Many people who listen to podcasts enjoy recommending them to others, including your librarians! Talking to people who regularly listen is a great way to learn about podcasts that might not appear on recommendation lists online.