As big of a Hawkman fan as I am (and I consider myself a pretty big one), I think WB's priority should be to first concentrate on other characters and getting a Justice League film made sans Hawkman. Then, once Justice League finally drops, do a Hawkman film based straight off of (or as faithfully as is humanly possible) Tim Truman's original Hawkworld prestige format mini-series. The film, like that story, would end with Katar and Shayera traveling to Earth in search of Byth.
Enter Justice League 2: The Sequel. I won't bother throwing out possible threats, but it would, of course, be a big one. Batman, knowing the current roster of Earth's heroes would be outmatched, would approache Katar and Shayera for assistance, who are staying as diplomatic guests of the U.N. while they conduct their search for Byth. Batman asks them for help, a request which Katar outright refuses, while Shayera isn't completely opposed.
Batman: "You can reach me here if you change your minds." More or less the last we see of them. Until...
Film's climax: heroes need help, and Hawkman and Hawkwoman drop out of the sky in a Hulk-like scene of total bad-assery. Explosions ensue, giant things get smashed up by big freaking maces, and the crowd says, "Whoa. Those two are pretty cool."
Then you do a proper sequel to Hawkworld entitled simply The Hawks, where Katar and Shayera finally manage to track down Byth. After that, you could do any number of things. Another Justice League film based around Invasion!, with Katar and Shayera pitted directly at odds with their home world of Thanagar (in addition to a myriad of other intergalactic threats), or even something more closely resembling "Starcrossed." Or something completely different altogether; it doesn't really matter much to me at that point.
The most important part in my mind, though, is properly laying the groundwork. That would be accomplished by making Hawkworld a truly atmospheric sci-fi film and waiting for a Justice League sequel to paint the characters more as actual super heroes. I would even want Katar to have a line like that when Batman is making his pitch for them to join the team: "We aren't heroes, and even if we were, this isn't our world to save."
As for personality, I prefer Katar being the ambivalent, short-tempered lone wolf to Shayera, who would be far more pragmatic and personable by comparison. These roles were reversed a tad from the Silver Age with Hawkworld (the comic book; not my hypothetical film), but I think the more classic take of Hawkman being the impatient brute whom Hawkwoman tends to keep in check is the more endearing one. So Hawkman would function as the reluctant warrior in the League, whereas Hawkwoman would be more of a team player, eager to lend a helping hand. And both of them would be all business and tact on the battlefield, with them working in tandem like no other two heroes in the film.
As for power levels, I'm fond of Johns' benchmark in Hawkman Vol. 4 of 20-times a person their weight and size's strength. It's a nice ambiguous number without being too ambiguous, firmly establishing them both as stronger than Batman but still substantially weaker than Superman. I'd also tweak the biology of Thanagarians to include organic wings (as both the animated Justice League series did, and now the New 52 has done), as well as categorizing Nth metal as ultra rare, reserved exclusively for high-ranking Thanagarian law enforcement officials, and only working on Thanagarians as a physiological enhancer.
Just my two cents. Thanks for reading (if you even made it this far, that is).