Val McDermid has written a number of crime fiction series in quite different styles, some standalone novels and non fiction.
Her series characters
Lindsay Gordon is a Scottish lesbian journalist who keeps finding herself caught up in murder investigations. These were first published by the Women's Press in the 1980s, apart from the last one which she wrote some years later after acquiring bestseller status. I really enjoyed them but they are of their time. Titles include Common Murder and Union Jack (#3). 5 books.
Kate Brannigan, is a private investigator working in South Manchester. There are 6 books about her. I like these for the settings, as I come from Leeds and lived in south Manchester as a student.
Carol Jordan and Tony Hill - police officer and psychological investigator. Serial killers. It took me years to try the first one as I wasn't at all sure about this change in direction, but I do like this series very much, though there was one that I found disappointing. This together with the standalone A Place of Execution were breakthroughs for her. Started in late 90s and now 11 books in series and ongoing.
Karen Pirie is a Scottish police detective. She first appears in The Distant Echo mainly set in the late 70s, though I think she's in the storyline set later - it's a cold case story. But I don't see The Distant Echo as really the start of the series because she's a character, it's not really focused on the police detective character/investigation as the 5 or 6 books that feature her as a central character properly are.
I really like her non fiction book A Suitable Job for a Woman about real female PIs and what they do in real life rather than in ficiton. bit I'm not sure whether it's in print.