I was the same way with my Droid RAZR Maxx and the Gorilla Glass had two small micro-scratches after a month or so. Nothing noticeable unless under direct LED lighting or something but annoying either way. I kept a dedicated pocket for my phone and the scratches still appeared so lesson learned. I use a Flip Cover (OEM) and call it a day. I'd rather go naked but this is the best option for me. Granted, I have a Note II now but I'm pretty sure we have the same Gorilla Glass.
I use one on my GSIII but just as much for dirt then for scratches. I use my phone everywhere and it's gotten everything from syrup to some glue type substance on it. Would've been a pain to clean the screen but I was able to just peel it off the protector and start a new.
Yes, the Gorilla Glass with the oleophobic coating on it will do a pretty damn good job of protecting your screen. No, your screen will not scratch 'for no reason.' Dust, sand, and very hard minerals will scratch it no problem.
Personally, I use the Pure-Gear screen protector on my S3. It was recommended to me by the Verizon salesperson when I bought the phone. You can barely tell that it's on there and if anything happens to your screen protector, you can go to any Verizon store and they will replace it for you for free because this has a lifetime warranty. One thing that I love about this screen protector is that it doesn't really show the fingerprints on it too much. I'm pretty anal about that on my devices.