The last major subsets of "firsts" among the fiction magazines that got me hooked were arguably books, most of them...Alfred Hitchcock's Mystery Magazine for January, 1978 was the first adult fiction magazine purchased for me new, 75c and the best bargain in fiction magazines at the time. And, unusually for AHMM covers of the time, it was competently composed...and there were memorable stories from Lawrence Block and Jack Ritchie, particularly. Inasmuch as I'd already collected some mid-'60s back issues, and read a few more borrowed from the Enfield Central Library, I was given the funds to buy a subscription...and not too long after, I was able to procure a copy of the first Alfred Hitchcock's Anthology, which many reference sources would prefer not to call a magazine, despite being issued periodically to newsstands by magazine publisher Davis Publications (who also issued Ellery Queen's Mystery Magazine and the Ellery Queen's Anthologies, which the Hitchcock item imitated), although a Dial Press hardcover edition was also published which tried to disguise the all-AHMM selections as one of the eclectic anthologies Robert Arthur and Harold Q. Masur would ghost for Hitchcock and Random House. These, instead, were edited by the magazine's editors...in the manner of the many previous Dell paperbacks taking their contents from AHMM.
The early AHA issues/volumes had a Very rich backfile to draw on, so you can see how addictive they could be, as well...at about the same time, I was not only also picking up new issues of EQMM and Mike Shayne Mystery Magazine, but was always happy to stumble over such treasures of the recent past as The Saint Mystery Magazine,,,and, several years later, in 1985, a clangourous new porject popped up, the New Black Mask, even as MSMM was beginning to go into its final tailspin, Each issue of New Black Mask, all published as books by HBJ, which would also sell you a subcription to the series just like a magazine, featured a remarkable mix of writers spanning the range of hardboiled and noir ficton and bit beyond. I actually picked up the last volum as NBM to keep first, then collected most of the rest as I catch could, and also the successor series, A Matter of Crime (after the trademark holders of Black Mask challenged NBM's right to use the title). 
I started reading the eclectic little magazines (as distinct from fantasy-fiction littles such as Whispers), aside from arguably Short Story International (which was a nonprofit that used good paper and charged twices as much for itself per issue than most of the other fiction digests...but it was on newsstands, unlike most littles), with TriQuarterly, which in its first decade particularly was offering one great issue after another, particularly when Robert Onopa was associated with the magazine, in the latter '70s. A snobbish backlash over the SF issue (Algis Budrys, Ursula Le Guin, Thomas Disch, Samuel Delany) severed most of the staff, including Onopa, from the magazine, which has yet to fully recover its quality of those years...the subscribers, I guess, had been pushed to their limits by the previous western (Dorothy Johnson, Cormac McCarthy, et al.), "Love and Hate," and other theme issues, including "Prose for Borges" and more. (TriQuarterly has gone web-only just recently.)
Of course, even before I began reading the little magazines that were no-bones-about-it magazines (such as also The Paris Review and Antaeus...it took me a while to find The Ontario Review and Boulevard and the comparitively dull Story revival), I had found some of the periodical book/magazine projects that had begun in the 1950s, such as New World Writing (the 6th volume/issue featured a long excerpt from Louis Armstrong's memoirs, contemporary Japanese haiku in translation, and more), 
and their modern descendents, such as the Doubleday Literary Guild loss-leader Works in Progress (which in the first issue I had offered the best chunk of Alix Shulman's Memoirs of an Ex-Prom Queen). I tumbled to New Directions and New American Review (later simply American Review) and Evergreen Review (in those largely post-censorial times) not long after.
...come to think of it, mentioning Evergreen reminds me of two other categories of fiction magazine that I haven't quite yet nostalgically surveyed...the humorous and the erotic (the latter had quite a vogue in the '80s and '90s, ranging from Yellow Silk to Paramour, from Future Sex to Blue Blood).
For more "forgotten" books this week, please see Patti Abbott's blog.
