So far Paul's story in Acts is the front runner, and I suppose that is not a big surprise. There have been a few attempts at the story of Paul, most notably Peter and Paul starring Anthony Hopkins as the man from Tarsus (and featuring in the Arts and Faith Top 100. There's also been Paul The Apostle made for the Bible collection, Paul the Epistle (made by the same people who made the Jesus film The Revolutionary), Anno Domini, and the Visual Bible's Acts not to mention "cameos" in 50s biblical epics such as Quo Vadis?. He also appears, albeit briefly in The Last Temptation of Christ. Of these Hopkins' portrayal is, as you would expect, the best by some distance. One other dramatic portrayal that I appreciate is the fleeting glimpses of him in some dramatised scenes from the BBC documentary St. Paul, although I hasten to add not the ones where he rolls around trying to illustrate the unlikely scientific theory that had just been proposed for Paul's Damascus Road Experience. (There is some discussion of these various films about Paul at Arts and Faith.
The difficulty with Jeffrey's question is that if it's not Paul, then there isn't so much else to go on. Sure, Mel Gibson made a two hour film out of the few chapters we have in the bible that cover Jesus' trial and death. But once you take Paul out, then nothing in the remainder of the NT has as much significance, or sufficient back story.
Probably the best remaining option is the story of Peter, but even with his key role in the Roman Catholic Church it's debatable whether there is sufficient tradition to flesh out his story as there is with Jesus's Passion.
The other option would be the life of John. This too has been attempted recently, again by the Bible Collection, in their series finale The Apocalypse (my review, hosted, as it happens, at Jeffrey's main site). There are certainly flaws with this production, but you can see what it is trying to do, and as such it is fairly admirable.
Given that both John and Paul have been covered recently, I would have to plump for a story around Peter.
As for a director, my choice would be a bit more straight forward. To really get the most out of the available story/tradition they would need to have some routing in Catholicism. In order to make a film that is interesting in itself, (rather than because of the controversy surrounding it, like The Passion) they would perhaps be better being slightly detached from the faith they were brought up in. There are a few candidates here, but perhaps the one with the best pedigree, and who would be most interesting would be...Martin Scorsese.