I'll nominate the first in the Phryne Fisher series,
Cocaine Blues, by Kerry Greenwood. It's only $.99 on Amazon.com, is available in audio format as well, and is the start of a simply delightful series.
Set in Melbourne Australia in 1928, the
Cocaine Blues features The Honourable Miss Phryne Fisher, along with a wonderful (and increasing over the series) cast of characters. The writing is elegant and witty, the characters very fleshed out, and it's truly one of my favourite series. The description from Amazon:
Spoiler:
From Publishers Weekly
The growing American audience for Phryne Fisher, Australian author Greenwood's independent 1920s female sleuth, will be delighted that her diverting first mystery is finally available in the U.S. Fisher's off-the-cuff solving of a high society jewel theft leads her to her first professional engagement when a witness to her brilliance asks her to investigate a possible poisoning-in-progress. The detective's admirable willingness to intervene to help those in distress involves her in a variety of other puzzles, including identifying the King of Snow, who has taken over the Melbourne drug trade. Many of the members of Fisher's entourage familiar from later novels make their debuts as well.
From Booklist
Australian Greenwood has been exporting her outstanding Phryne Fisher series to the U.S. for the past several years, but the books haven't arrived in chronological order. Finally, we have the series debut, which explains how the irrepressible flapper (the series is set in the 1920s) became a detective. Phryne fans will relish the chance to see how beloved characters like Bert, Cec, Dot, and Inspector Robinson wandered into Phryne's life, and newcomers will enjoy getting to know ultrafashionable Phryne, who's wealthy enough to do whatever she wants but whose previous poverty has created a strong empathy for the working class. In Melbourne to investigate the mysterious illness of the daughter of a family friend, Phryne stumbles into a case involving two of the 1920s' signature evils: cocaine and back-alley abortions. Banding together with a crew of colorful local characters, and finding time to indulge in some erotic fun with a sexy Russian dancer, Phryne soon leaves her mark on Melbourne. From beginning to end, Greenwood infuses her series with evocative settings, multidimensional characters, and satisfying mysteries.
Kobo link. It's $1.03 at Kobo Canada, but couponable.