I said this in the other thread, but I think the best way to go about doing a Hellblazer film would be to make it a lower-budget British horror film. Set in England, shoot over here, and get a Brit cast. I think with a grubby London aesthetic would be far more atmospheric than Los Angeles gloss, and would feel more authentic to the tone of the comics.
As far the plot goes, I actually wouldn't try to go into exploring Constantine's origins, or go too large-scale with something involving Nergal or epic battles with all Heaven and Hell. I'd scale it right back, into a standalone horror tale of people plagued by some demonic/supernatural occurence. You spend some time establishing that, and Constantine is brought in at the start of the second act as the enigmatic figure you might have a solution.
In terms of casting, I'd go for Paddy Considine. The guy is one of the most dependably great actors working today, and he's currently in that stage in his career where he can play the lead in smaller films or be a supporting character in bigger films, one pivotal role shy of taking his career to the next level. Constantine could be the perfect role: even the names match up.