Aggressively personalized (but not saturated by my more eccentric tastes), this is my Comic Book Starter Kit.
The assumption is made that you are familiar with the “core works”¹, at least in name, and that almost anything anywhere will recommend them to you if you bring up comics.
Some other caveats:
This is Western-focused. That’s where most of my experience is, and it tends to be what’s at issue in discussions of “comic books”. This doesn’t degrade or dismiss the works of even slightly-less-west Westerners (like Hergé or Goscinny/Uderzo, and so on), nor is it intended to imply a superiority. It’s just that those are not typically considered “comic books” but other forms of what Scott McCloud so succinctly and clearly defined as “sequential art”.
Now, with all that said:
Legitimately one of my most recommended titles–even by proxy, as I recommend writer Mike Carey’s Felix “Fix” Castor books a lot, too–Lucifer is an elaboration upon the devil developed by Neil Gaiman in the Sandman (see, that’s how cornerstone that book is). The titular character is not always even the protagonist, nevermind being a hero. He’s cold and cruel but ultimately disinterested in that which does not serve him. He maintains a semblance of sympathy or identification anyway, though, as he seeks to blaze his own path in the universe, unencumbered by the identity and occupations God has set for him. What it has over on books like its “parent” is a pretty absolute focus: while it encompasses a 75-issue comic, a 3-issue miniseries, and a one-shot, it is a clearly defined overarching story–while things like The Sandman can have some problems with meandering off into side-stories and experiments Gaiman found interesting (albeit successfully!).
2) Swamp Thing (“Saga of”/Volume 2, ~20-64)
To my strange and peculiar tastes, this is the crowning achievement of Alan Moore. It sits next to Marvelman/Miracleman comfortably, in his 80s run of respectful reinvention. It, for all its horror, doesn’t have anything as unpleasant as Miracleman‘s climax (about which I will say no more, but it’s filled with graphically violent images–earned and ‘necessary’ to address the story and its point, it should be said, but nonetheless disturbing) and has a significantly larger amount of emotional investment, as well as the genesis of the great John Constantine (whose name can be ‘heard’ pronounced by the demon Etrigan: it’s Constan”tyne” not Constan”teen”)
3) The Maxx
Sam Kieth is a peculiar artist, and a peculiar storyteller. What was advertised at the time (I was about eight, myself) was “a violent new hero”. What was offered was a strange book about a large purple-and-yellow homeless guy who was friends with a social worker, the two of them harassed endlessly by a smugly knowledgeable sorcerer/serial rapist. The latter part isn’t involved overly graphically, nor as a means of conveying “edgy” material, so much as being part of overarching themes. It’s a difficult book to describe without simply giving it all away, but it’s filled with Sam’s unusually wonderful art, aesthetic and ideas.
4) Animal Man (volume 1) 1-26
Grant Morrison’s breakout work, it’s unusual in the extreme and does suffer from some of Morrison’s preachiness, but can be somewhat excused by its well-executed relevance to the main character. It’s definitely in the realms of “required reading”, in any case. It’s another where you’re best off just reading it without knowing too much.
5) Daredevil (Miller/Janson: v1 158-191, 227-233; Bendis/Maleev: v2 26-81)
The first (Miller/Janson) is classic, in all senses. The peak of Miller’s writing (sadly, at the early end of his career…), and perfectly matched with his own pencils or Janson’s, and definitely Janson’s inks. Matt Murdock is absolutely put through hell, and the depths of his dealings with Wilson “The Kingpin” Fisk (who was originally a Spider-Man villain, but lost almost unequivocally to DD at this point). Bendis and Maleev’s is a thematic return to this, with perfect art for the story from Maleev.
6) Justice League ([America|International|Europe])? (1-6, 7-25, 1-36, 26-60; Formerly Known as the Justice League 1-6, JLA Classified 3-9 [“I Can’t Believe It’s Not the Justice League”], now Justice League 3000 1-15, Justice League 3001 1-ongoing)
Keith Giffen and J.M. DeMatteis, one known most for comedy, one known most for pathos (though both are capable of either and both) take the Justice League denied its most famous elements (no Superman, Wonder Woman, The Flash, Hal Jordan or John Stewart as Green Lantern, and even Batman only lasts a few odd issues) and turn them into a bumbling, inefficient group of also-rans filled with heart, will, desire, jokes, comedy, and actually a fair bit of oft-unremembered real drama.
7) Planet Hulk (Incredible Hulk v3 92-105, Giant-Size Hulk #1)
Requiring some of the most minimal of background, the Hulk is unwittingly exiled from Earth by its foremost minds and his foremost–seeming–friends (Tony Stark, Reed Richards, et al). Stuck on a hellish planet, Hulk is forced to find his way through the minimalist society that exists there, and is driven by a raging need to take revenge on those responsible.
8) Suicide Risk
Mike Carey has written superhero books for the Big Two, but this was his own creation. And yet…it turns out it just may be something entirely other than a super hero book as it goes on. Another self-contained and clean series by Carey.
9) The Question
Dennis O’Neill is responsible, somewhat more quietly than a lot of the Brits who followed him and were eventually his contemporaries (or writers under his editorship) for a lot of classic works. But his peculiar book with penciler Denys Cowan is an achievement outside the shadow of characters like Batman. Sure, Ditko invented the rather ridiculous Objectivist Question decades earlier, but O’Neill’s unusual take on Vic Sage is more philosophical and interested in the world as it actually functions, and is married to the signature pencils of Cowan.
10) Current ongoings:
Rick Remender’s anything (Black Science, Low, Deadly Class, Tokyo Ghost)
Descender, Black Magick, Copperhead, Manifest Destiny, Rat Queens, Rumble
¹Sandman, Watchmen especially. Other Moore can be an acquired taste, some moreso than others, but Watchmen is a medium-defining moment.