If you have scratches on the screen already, they will still be visible with a screen protector.
I would suggest you buy a replacement screen - cost about $40 USD give or take a little depending on your country - put a screen protector on as soon as you swap it out.
For fine scratches, a wet-apply protector (like Skinomi) may hide them. I have a few from initial usage (I was impatient when I got it), but can't see them through the protector. But then the Skinomi skin is a little bumpy to start with, so it may be hinding them just be being what it is.
The one thing I love about this brand is that if new scratches happen on the skin, the skin eventually (about 15 mins) re-bonds and melts back together. I'm not sure of how it works, but I have had a couple of instances now where I scratched the protector pretty bad and figured it was hosed, and an hour or so later it was like it never happened.