Mystery writers I’d go out of my way to read, in order of preference:
Josephine Tey
Edgar Allen Poe
Raymond Chandler
Dashiell Hammett
Ross Macdonald
Ian Rankin
Peter Robinson
Ed Mcbain
Arthur Conan Doyle
Kinky Friedman
Elmore Leonard
Begging your pardon - do you mean J. S. Fletcher? Or am I being whooshed?
There is a Richard Jay Parker, who wrote the one novel ‘Stop Me’ in 2009.
My nominations:
Sir Arthur Conan Doyle
Agatha Christie
Ellery Queen (*The Greek Coffin Mystery *is at least as radical in its approach to the “Golden Age” mystery as The Murder of Roger Ackroyd)
Dashiell Hammett
Raymond Chandler
Ross McDonald
James M Cain
PD James
Marcia Muller
Kate Wilhelm
Cynthia Harrod-Eagles (Slider is highly underrated)
Sharyn McCrumb (for the Ballad and Jay Omega novels, not the wretched Elizabeth McPherson shit)
I myself will be voting for PD James who, IMO, has raised the detective story to the realm of literature.
Ah, got it! :o 
I’ll take that one off the list, then, shall I?
(It’s part of the fun, running into writers that I haven’t even encountered before that other people feel should be nominated. Makes me want to chuck all this holiday season bollocks and hide in the library for a month…)
And the run-off poll can be found at this link. Poll to follow within the hour.
Closed at the request of the OP.