I think most people have already given the most obvious ones such as weapon or suit customisation, so I'll try to think of different ones,
Shooting through peepholes in doors when someone comes to answer it. Let's say you knock on the door or ring the bell, you can press the gun up against the peephole and fire through it when prompted.
Instead of having the briefcase only, it'd be nice if we could use backpacks or small crates to store weapons in and carry them about. It doesn't make much sense for 47 to be dressed as a tourist carrying a briefcase.
Enclosed maps like Paris should have starting areas such as safe houses. Although I would like it if every mission had a safe house.
Bigger storage cases. Instead of being able to fit a single sniper rifle in one large cases, we should be able to store a sniper rifle and two small weapons/items inside them. Or five small weapons/items inside a large if you choose to (I play contracts quite a lot and it gets kind of frustrating having to choose between a sniper rifle, a lockpick, poison or explosives, it'd be nice to have multiple choice).
More storage locations. Instead of one storage case in one location, it'd be nice to have multiple cases.