Why doesn't Vincent kill Annie first?
On rewatch, a friend noticed that Max picks up Vincent right as he drops off Annie - which is to say Vincent was already at the location for the first of his targets.
Why does he save her for last instead of killing her first?
And even if there's a reason for that, why does he go to her building first?
He was likely researching the location she would be at. Note how he basically tests the key card he needs to enter then building and then leaves. He also cannot kill her there and then, it would be too much in the open. It would also trigger a much larger police action, unlike when he first kills a number of underworld-related characters.
Of course, from a story point of view, it happened like that so there would be a surprise later on in the movie when it turns out that his final target is the woman we met early on in the movie.