You can find many MP3s of the old time radio shows on the internet, to give you a taste of good shows and bad shows. Do a search and look around. You should be able to find some Jack Benny, and some Shadow for sure. They were on the air for so long, and have so many fans.
The Shadow was a popular long running show based on a pulp character that was in novels at the time. The show had high production values. Some lesser made shows would have a narrator say things like “And Jill opened and closed the door and walked over to the desk”. The Shadow would have sound effects guys who actually made you hear Jill opening and closing the door. They were able to put more of it into your mind’s eye. Problem with The Shadow is that it’s stories are rather silly, listened to today. If you get over how hokey the plots are, they are well made and enjoyable to listen to. The first couple of years Orson Welles stars as Lamont Cranston. I believe Agnes Moorehead plays the female lead, but I am not sure.
Speaking of Welles. The Mercury Theatre had some well done performances. Aside from it’s most famous(infamous) War of the World’s show. There are numerous stories from classic literature that was redone by the Mercury Theatre players.
Johnny Dollar is a fun show. Johnny Dollar is an insurance investigator. The framework of the show is Dollar writing up his expense list for the latest case he worked. Justifying all of his purchases and explaining what happened in the case. This, I believe, started out as a 5 day a week serial. Each day there was a 5 or 10 minute show that had a cliffhanger at the end to be continued the next day. It was turned into a regulary 30 minute show, eventually. The 30 minute show is much better than the serial.
I think a fun well made show that you don’t hear about a lot is Damon Runyon Theatre. These are stories based on the stories of Damon Runyon. Guys and Dolls is based on Damon Runyon’s stories. The stories are told through the eyes of a narrator named Broadway. They mostly tell tales of the New York underworld. Nothing gritty, just fun stuff.
Good luck. I hope you find something you like.