Here's the "other" convoluted character whom no one can seem to sustain over a long period of time, at least in the eyes of the public.
Hawkman's had just as many variations as Aquaman, or nearly, and in collating those histories and various "looks," the character has become schizoid. Writers James Robinson and Geoff Johns took all the different Hawkman conceits (at one time Hawkman's real identity was Carter Hall, archaeologist and reincarnated Eygptian Prince...then he was Katar Hol, an alien called a Thanagarian, a policeman studying our crime-prevention methods, and later refined as a policeman pursuing a deadly criminal to Earth, and so on) and smashed the ideas together, which is perhaps the last time the character has been rebooted for a modern audience.
Hawkman's persona has ranged from stoic leader to barbarian warrior. He's been intelligent, he's been salt-of-the-earth, he's been conflicted. He's been benign, he's been malignant. His costume has ranged all over the place, with the primary difficulty in presenting a man with big (fake) wings being less visually clumsy and more workable.
I think the thing with superhero comics, and superheroes in general, is a combination of persona externally represented by the costume...meaning, the best superheroes act like they look.
Most writers will give you the Bad. "Bad" is how us 1970s kids would describe something that today is "cool." Cool used to mean how somebody acted...the Fonz was cool, nothing rattled him. "Bad" was usually said as "He is Baaaaaaad." Meaning, usually, tough. Especially in a fight. If you were "baaaaaaad," you didn't have to worry about anything.
Comic book writers in general will give you plenty of "baaaaaaad" but surrender the common sense and internal logic of the characters to do it. Batman has suffered mightily because of this preoccupation. And a psycho-anal world of soft-guts says that to be "bad" one also has to be "disturbed." Batman becomes a bit of a loon to justify kicking criminals in the face. This characterization becomes rote, eclipsing the more structured and balanced notion of the "Dark Detective" which the character fostered post-1950s until the 1980s. Basically, Batman lost his "cool" and kept up the "bad."
Hawkman flies using "Nth Metal," a Thanagarian alloy which allows anyone wearing it to defy gravity. This also provides somewhat superhuman strength. The Carter Hall archaeologist version is conversant with ancient styles of warfare and weaponry. He enjoys hitting people with a big spiked mace. Who wouldn't?
That's Hawkman's "bad" right there. He's a reincarnated man from all different eras of history. He's fought in every conceivable war, he's experienced every unconceivable heartbreak. He's also got a woman, his Hawkgirl, usually reincarnated with him in whatever era Carter Hall is in. At some point, the two of them are murdered and will once again be reincarnated, this cycle to occur over and over as the two lovers are forever cursed.
It's a bit heavy, especially for your "new" reader...various writers over the years have sought to remove the unwieldy aspects. Like Aquaman, Hawkman suffers from audiences who really shouldn't have that much of an influence on his comic book. I'm speaking of adults who have clung to the various Hawkman versions and refuse to acknowledge any Hawkman that doesn't represent, in some way, their Hawkman.
Way to murder the future of comic books, fellows.
I never really thought much about Hawkman when I was a kid, but I wasn't that smart as a kid. From the viewpoint of new readership for comics, and my current affection for the character, I'd probably get rid of a couple aspects of the overall character, like the curse thing (which may have already been solved.) Also, I'm not a big fan of the Hawkgirl dynamic. I can't help it, but knock-off versions of male characters grate on me...they're rarely able to step out of the shadow, and since there's so few really good original female characters...well, Hawkman wouldn't have Hawkgirl.
The other point: Hawkman's environment is off. Currently, or at least as of the last of his solo series a couple years ago, Hawkman lived in the DC Comics version of New Orleans, a place called St. Roch. Fine and good, except when you look at Hawkman, or when I look at Hawkman rather, what you see is a character who makes much more sense in exotic locales. He's been in a Science Fiction setting, he's been in the big city, he's been stationed on a satellite in space...where Hawkman works would be a kind of Indiana Jones world of international intrigue. Carter Hall should be a fairly nondescript dude, like Indy Jones in his civilian life, but once he's Hawkman, he's in the deserts of Cairo punching Nazis into airplane propellers.
Unlike Tarzan, who actually works better outside of the Jungle, Hawkman would be perfectly suited to life in a unpredictable Savage Land, preferably packed with hyena-men and wicked monsters. But yet intricately connected to "our" dimension and reality...Hawkman would rule Monster Island while having no idea of what was around the corner. A Hawkman who has never seen this landscape has to survive in it.
To me, that's the core of Hawkman according to his external motif: he's a survivor, a fierce predatory survivor in point of fact. He should be one of the most savage, and adaptable, superheroes in comics.