IMO your hand position should be such that your forearms are perpendicular to the bar with your elbows brushing as close as possible to your torso during the press.
Any closer than that and you actually have to limit your range of motion and flare out your elbows just to touch the bar on your chest. When you flare out your elbows on close grip bench, you actually take emphasis off the tris and onto your chest. When I was taught to bench close grip, I was told that the elbows stay tucked in as much as possible throughout the whole movement.