The softer the screen protector, the more shock it will absorb. (Hard protectors protect against scratching. They do sometimes act as sacrificial screens, breaking instead of the one on the phone, but many times, a fracturing tempered glass protector takes the phone''s screen with it.)
I'd go for an Otterbox case and, if you insist on a protector, a 3/$5 pack of plastic ones. (I've dropped my phone pretty hard in an Otterbox - what would have been "oops, I need a new phone" without it became just "oops" with it. Even screen-down on a brick walk.)