I don’t know about recommendations; there’s so much out there that you can’t really go wrong with just taking a glance through lists of mysteries and picking out ones that sound interesting. My favorite is probably Chesterton (google Gutenberg Chesterton, and you should find a catalog of all his public domain stuff for free), but that’s because his prose is very unique; I’m honestly not sure how interesting his writing will be. I love it to death, but I’d imagine it varies.
He’s a great place to start, if you want to check out the “extremes” that you won’t really find anywhere else. For the more usual stuff that you’d expect from classic and modern authors, you should try Christie (her stuff’s the general “Golden Age of Mystery” kind of writing), The Maltese Falcon (a great example and highlight of the “hardboiled” mystery genre that gained weight in the 50’s and onward, after the decline of the Golden Age), and perhaps one of the more popular current mysteries; you can find them on Amazon or in your local bookstore (generally more psychological: like The Girl in the Train, I think it’s called? Haven’t read many of those kinds). I’m admittedly not as well read in the current mysteries, given they cost money I don’t have right now, but there’s a lot out there.