if you had to pick just one...

I find that the poetry in literary mags leaves a lot to be desired. Then again I am not a poet, so my opinion of academic and nature poems may be off base. My tastes in mags fluctuates. I loathe Zoetrope, but I find that I have been reading a lot of issues of Ploughshares and The Threepenny Review lately.

No mag hits it right though. I'm not upper or middle-class, and the literary fiction aimed at lower class folks such as myself tends to be of a lower quality, and mostly relegated to e-journals because of the overhead costs for a print-mag. A good story is a good story, but man it seems 85% (random stat) of literary fiction journals are just plain incestuous in terms of story content. I say this as a reader, I usually ignore it as a writer.

One Story. I like it even more than Glimmer Train.

Just one

Tough choice, but either Southern Review http://www.lsu.edu/thesouthernreview/

Or American Poetry Review http://www.aprweb.org/

By "literary" do we mean the literary genre, such as it is? Or can any genre work?

ANY genre, I'd go for the Magazine of Fantasy & Science Fiction.