Schmitz wrote mostly short stories, which sold chiefly to Astounding Science-Fiction, which later became Analog Science Fiction and Fact, and to Galaxy Science Fiction. Gale Biography in Context called him "a craftsmanlike writer who was a steady contributor to science fiction magazines for over 20 years."
Schmitz is best known as a writer of "space opera", and for strong female characters (such as Telzey Amberdon and Trigger Argee) who didn't conform to the damsel in distress stereotype typical of science fiction during the time he was writing.
His first published story was "Greenface", published in August 1943 in Unknown.Most of his works are part of the "Hub" series, though his best known novel (Gardner Dozois, long-time editor of Asimov's Science Fiction magazine, said it "is usually thought of as Schmitz's best work") is The Witches of Karres, concerning juvenile "witches" with genuine psi-powers and their escape from slavery. Karres was nominated for a Hugo Award. During recent years, his novels and short stories have been republished by Baen Books, edited and with notes by Eric Flint.
In an introductory essay comparing Schmitz with contemporary author A. E. van Vogt, Dozois wrote, "Although he lacked van Vogt's paranoid tension and ornately Byzantine plots, the late James H. Schmitz was considerably better at people than van Vogt was, crafting even his villains as complicated, psychologically complex, and non-stereotypical characters, full of surprising quirks and behaviors that you didn't see in a lot of other Space Adventure stuff."
And his universes, although they come with their own share of monsters and sinister menaces, seem as if they would be more pleasant places to live than most Space Opera universes, places where you could have a viable, ordinary, and decent life once the plot was through requiring you to battle for existence against some Dread Implacable Monster; Schmitz even has sympathy for the monsters, who are often seen in the end not to be monsters at all, but rather creatures with agendas and priorities and points-of-view of their own, from which perspectives their actions are justified and sometimes admirable—a tolerant attitude almost unique amidst the Space Adventure tales of the day, most of which were frothingly xenophobic.
John Clute writes in the The Encyclopedia of Science Fiction,
From 1949, when "Agent of Vega" appeared in ASF as the first of 4 stories later assembled as Agent of Vega (coll[ection] of linked stories 1960), he regularly produced the kind of tale for which he remains most warmly remembered: Space Opera adventures, several featuring female Heroes depicted with minimum recourse to their "femininity" – they perform their active tasks, and save the Universe when necessary, in a manner almost completely free of sexual role-playing clichés. Most of his best work shares a roughly characterized common background, a Galaxy inhabited by humans and aliens with room for all and numerous opportunities for discoveries and reversals that carefully fall short of threatening the stability of that background. Many of his stories, as a result, focus less on moments of Conceptual Breakthrough than on the pragmatic operations of teams and bureaux involved in maintaining the state of things against criminals, monsters and unfriendly species; in this they rather resemble the tales of Murray Leinster, though they are more vigorous and less inclined to punish adventurousness.
Greg Fowlkes, Editor-In-Chief of Resurrected Press, adds, "During the 50's and 60's "Space Opera" and James H. Schmitz were almost synonymous. He was famous for his tales of interstellar secret agents and galactic criminals, and particularly for heroines such as Telzey Amberdon and Trigger Argee. Many of these characters had enhanced "psionic" powers that let them use their minds as well as their weapons to foil their enemies. All of them were resourceful in the best heroic tradition."
This is a reasonably good synopsis. One thing I find worth noting is that many men who write "strong female characters" write competent adventerous women who none the less want nothing more out of life than to settle down and have babies (Robert A Heinlein I'm looking at you right now), present these women as special cases who stand out from ordinary women by right of being almost but not quite as competent as the men (Robert Heinlein I'm looking at you), and loudly proclaim to the world how very special they are for writing these strong female characters (Bob Heinlein, looking at). Schmitz did none of that. Trigger Argee had an one-again off-again relationship with her fiance/husband/boyfriend, Telzey Amberdon was only aware of men, women, or people in general to the degree that they gave her any trouble in life, and Grandma Wannattel was too involved in her business to worry about relationships. They rarely needed rescuing, and when they did it was from problems of a scale that Schmitz's men needed rescuing from as well. And Schmitz never presented the women he wrote as oddities, and didn't demand rewards for writing these characters.
There is some baked in sexism in the stories but it's clear that Schmitz regarded women as fully human, a feat that eludes many speculative fiction writers today. His stories and attitudes are in many ways less dated than the reactionary cyberpunk genre of the '80s and '90s, and the deliberately sexy Trigger Argee is a far more rounded character than the fighting fuck toys* of today.
I'll review the Baen editions of his stories, since they're the easiest to find these days. But James H. Schmitz's stories were heavily reprinted in anthologies through the '70s and '80s and can be found in used book stores or online. Some of his stories are also available for free online, since they've fallen out of copyright. First up, The Witches of Karres, the book that George Lucas ripped off for Star Wars before he started ripping off Akira Kurosawa
* YouTube link. The video is horrible quality, but it's the only clip I could find of that part of the interview.