One thing you may want to consider about crime fiction genre is that a very common practice amongst its authors is to develop a character over a lengthy series of novels that are not, in other ways, specifically narratively connected. Michael Connelly's Harry Bosch novels can be read pretty much in any order without losing anything besides a bit of character history, for example. So, look closely at books that may outwardly appear to be described as part of a series. They aren't usually connected in the way that a sweeping epic space opera or fantasy would be.
Anyway, here's a few I really enjoyed:
Anatomy of a Murder by Robert Traver (50's court case from the lawyer's perspective)
The Hunter by Richard Stark. This is more noir than mystery. "Crime novel" is a fitting description though.
Gorky Park by Martin Cruz Smith
The Concrete Blonde by Michael Connelly
Presumed Innocent by Scott Turow. It's best if you haven't already seen the movie, but still a fantastic novel even if you know the outcome.
The Alienist by Caleb Carr. Really fun historical mystery. It ventures into the dumb on occasion, though, so, you know, don't expect a lot of plausibility here. It's Fun.
The Motive by John Lescroart. Lawyer's perspective novel. Solid and entertaining but not blow you away fantastic in any respect.
Of course the all time classic: Crime and Punishment by Fyodor Dostoevsky.