Is this series a good next step, or am I better off reading something from his back catalog first?
1) Watch "No Country for Old Men" (and optionally read it - it's a very faithful adaptation but you'll get additional character motivation/backstory from the book)
2) All the Pretty Horses - bildungsroman of two teenage boys chasing a way of life that no longer exists. One of his more accessible works, and the one that made him famous outside of literary circles.
3) Child of God - a light, quick read with a sympathetic portrait of a necrophiliac cannibal.
4) The Road - This will hit especially hard if you're a parent. A beautiful novel about not giving into despair no matter how dire the circumstances.
5) Suttree - in some ways the mirror of All the Pretty Horses - a young man leaves his way of life when it becomes clear that said way of life is vanishing. Based on McCarthy's real-life experiences growing up in Knoxville. Easily his funniest book. Probably the most compelling description of a specific milieu (1950s Knoxville underclass) I've ever read - simultaneously accessible - there are people who lived that life who are still alive - and yet impossibly remote.
6) Blood Meridian - Hard to describe. I wouldn't read Blood Meridian first because it's quite difficult, and because it has a way of making everything else (like...everything else, not just his other work) seem not as good.
Blood Meridian: easy to describe truthfully, hard to do justice to in that description.
Easy description: A Western. The western. One of the great masterpiece novels. Set in the Texas-Mexico border area, circa 1850, beautifully lyrical writing, but is also an appallingly violent work, certainly the single most bloody book that I have ever read.
"A major theme is the warlike nature of man". https://en.wikipedia.org/wiki/Blood_Meridian#Violence
If you like his bleak, Hemingway-inflected style I'd suggest trying the short stories of Joy Williams ("Visiting Privilege").
I'm actually thinking of reading his entire collection, I've been so impressed by him. I just got No Country for Old Men.
Cool to hear the rec for Sunset Limited!
My personal early-style favourites: "Child Of God", "Blood Meridian" (of course), "The Crossing"
Later style: "The Road"
Interested to try some things from the mythological early style!