Hey, Natman.
If you're not averse to older works, the
University of New Zealand has a wide, if somewhat idiosyncratic selection of contents from various magazines, from
The Atlantic Monthly to
Weird Tales. You can pick and choose at random from mainstream, mystery, s.f., fantasy and horror, among others.
For myself, I'd suggest a couple of recent story collections:
A Feast of Sorrows by Angela Slatter (fantasy, horror)
Ghost Summer by Tananarive Due (s.f., horror)
A bit older,
In the Palace of Repose by Holly Phillips (fantasy, s.f.)
In the Forest of Forgetting by Theodora Goss (fantasy, fairy tales)
The Ladies of Grace Adieu and Other Stories by Susannah Clarke
If there is older work that can be regarded as essential,
The Martian Chronicles by Ray Bradbury (s.f.) would be one. Isaac Asimov's
I, Robot, Clifford Simak's
City and Robert Heinlein's
The Past Through Tomorrow would be others, as would any decent collection of H. G. Well's short work.
And there are a lot of recent anthologies that would give you a grounding in work valuable to the progress of s.f. and/or fantasy:
The Big Book of Science Fiction edited by Jeff & Ann Vandermeer
The Weird edited by Jeff & Ann Vandermeer (if you're interested in what's come to be called Weird Fantasy)
The S.F. Hall of Fame, vols. 1, 2A and 2B were go-to volumes for a quick introduction to s.f. when I was first reading s.f. and would give you a decent idea of the genre up to about 1970.
I'm sure there are other volumes, and if you check the forums here for threads on s.f. recommendations and
"Essential Anthologies" you'll find a lot of suggestions.
Randy M.