Oldman is apparently a nice, gentle person; I'm guessing/hoping he's a good dad. I also heard an anecdote of him being spooked enough by an earthquake during an L.A. film shoot that he took his lunch into the middle of a parking lot, far away from anything that could fall on him if another earthquake hit.

That gentleness, combined with the sort of psychos he can play, comprise the reason he was such a good choice to play Sirius Black, I'd say.