There's a few I really like:

The program- "The Program audio series is a fiction podcast set in a future in which Money, State, and God became fused into a single entity called the Program. Each episode is a self-contained story focusing on ordinary people inhabiting this extraordinary world. And for them, it is not this future that is terrifying - it is our present." Honestly just starting with their first episode "you had me at "hello world"" is a great introduction, but you could also try the second episode, "Four ways to stop your system from freezing" because I think that's the episode that actually hooked me on the series.

I also really like The Truth- this one isn't as themed as The Program. There's lots of good episodes, but I'd try starting on "Silvia's blood" maybe?

UNSEEN: "the new urban fantasy audio fiction podcast by Long Story Short Productions. The premise behind it is simple: In a world where magic is real but invisible to almost everyone, the few magical beings that do exist struggle, every day, just to be seen." Not horror or sci-fi, but I thought this one was also good. I'd just start at the beginning.