I never post on these boards, but I thought I'd throw my $0.02 in since Hawkman happens to be a favorite of mine.
The way I would go about making a Hawkman film is using the Golden Age version of both Hawks, Carter and Shiera. Use their Egyptian back story as sort of a prologue, perhaps fleshing it out further via flashbacks strewn in throughout the film as the two characters' "memories" come back to them.
I'd leave "Hawkgirl" out of it, however, keeping her in only as Shiera Sanders the reporter until the very end, where a superheroing career of her own could be hinted at for a potential sequel. That's not to say she couldn't throw down, however. Heck, she could even save Carter in a surprise move when a certain memory comes rushing back to her near the climax. But I'd leave a costume out of it for the time being.
The most important part, though, is I would set the film in the past, sort of like Cooke's New Frontier, but perhaps even further back than the '50s and 60s. I just think a 1930s or thereabouts setting would give the film a unique, noir-style edge that other superhero movies thus far haven't offered. Perhaps the archaeological angle gets me in an Indy sort of mentality, but for some reason this is how I've always thought a Hawkman movie should be done.