Poor Hawkman. This dude has been rebooted, what, three times at least? More if you count Hawkgirl/Hawkwoman as essentially reboots of the character.
In his career, Hawkman has been an archeologist (Carter Hall), a space cop (Katar Hol), and an angel (Zauriel). Weirdly, he tends to be presented as some sort of super-gruff, violent Wolverine-type character, which is pretty much at odds with what I think of when I think of an archeologist. Maybe you can get a bit of 'contempt of cop' fueling Hawkman's rage in his Thanagarian formation, but I dislike space cops for all the reasons I outlined in the Green Lantern entry. The angelic version is pretty interesting, but that opens wide a whole lot of doors that are best kept barely cracked (so Phantom Stranger can flit through).
So what is the Essential Hawkman? Muscly dude with wings, a bird hat, hand to hand combat, and a bad temper. Really, I see him as a sort of flying Conan and that's the frame we're going to build him around. I think the Conan model works well for Hawkman - he doesn't seem to have any notable supervillains all his own, so he needs to be a bit more proactive when it comes to his stories. So instead of Stopping Bad Guy X's Plan adventures, Hawkman will be more This Is Another Fine Mess I've Got Myself In To.
Let's get Carter Hall into a mess of Nth Metal to start. As mentioned in the Captain Atom entry, following the arrival of Superman on the world stage and the revelation that he isn't human, searching for alien artifacts from previous visitations has become a pretty big deal. Reverse engineering alien technology has allowed some aspects of science to progress by leaps and bounds, so it stands to reason there is a market for all that old junk. So our Carter is not an archeologist so much as a professional treasure hunter/tomb robber.
Carter spends much of his early career acting as a sort of consultant in the legally grey area of artifact reclamation. He travels the world helping governments and other organizations get a their grubby paws on alien artifacts and played a part in not only the recovery of the powersource that made Captain Atom what she is today, but the ship that lead to the creation of the August General In Iron in China.
He would almost be a noble rogue Indiana Jones figure if it were not for the fact that he's using these government-sponsored travels as a cover for his own hunting. Carter has in his possession a Victorian journal "liberated" from the British Museum that once belonged to Jim Craddock. It seems that back in the day, Gentleman Jim raided the Museum's collection and sold of many strange and wondrous items discovered in an Egyptian tomb by Napoleon's soldiers and later taken as spoils of war by the victorious English. Carter now has the clues as to where these artifacts are and from their description, knows they're worth a pretty penny.
Carter's quest to track down the missing Implements of Osiris will make a nice back-up feature for his title. Needless to say, he of course obtains an almost full set of Nth Metal tools, thus getting the bits he needs to become Hawkman. The Nth Metal lets him fly, helps him regenerate, makes him stronger, all that good stuff. Also, Nth Metal is sort of like a psychic sponge, absorbing the memories and knowledge of its past users. This is where Hawkman's "past lives" come in to play - he's not a reincarnation of an Egyptian prince, he just has all the dude's memories via the Nth. The more Nth metal the previous user had, the easier it is for Carter to access their memories. Thus Prince Khufu looms large because he had an almost complete set, but with some effort, Carter can access the other users' who only had one or two items.
Which is convenient, if you think about it, as most of the people who bought the items from Jim Craddock also had other treasures hidden away, which Carter now knows about. Hawkman in a Rogues In The House-style fight against a steampunk gorilla as he tries to raid the hidden lab of a forgotten Civil War inventor? Yes, please. He may also be able to access the memories of those whom he uses the weapons on, but we'll save that ability for a power-creep upgrade down the road.
As for recurring foes, we've got Gentleman Ghost who no doubt wants his journal back, plus the mysterious Hath-Set. In the Drewniverse, Hath-Set isn't so much a person anymore, instead he's the psychic imprint of the murderous priest from Khofu's days. The one Nth Metal artifact Hawkman lacks is Hath-Set's sacrificial dagger, an object that absorbed not only the priest's memories but his will as well. Now the dagger can control those who wield it and it wants more Nth Metal to add to its power.
So there's Hawkman. The only thing missing? Hawkgirl. I'm still on the fence about to deal with her. I suspect I'll follow the lead of the DCAU and have her be an actual alien from Thanagar, rather than some dude in a bird suit. If I did that, I'd make her an agent of the Thanagarian Empire sent to Earth to reclaim its lost Nth Metal possessions, which would make her start out as an antagonist to Carter Hall despite being pretty much like him, except on a galactic scale.