I put an ifrogz screen protector on my GS4 when I got it because that's what the AT&T store had. I ordered some iSmooth screen protectors for when I need to replace the ifrogz. I previously used them on my GN2 and liked them. I prefer the dry application over the wet application methods. I just use my microfiber cloth to clean it every now and then.
More to the point is finding a case that I like. I put the Speck Candyshell on mine (about the best of the few choices at the store) but don't like it. Too slippery for me. I want something minimalist that I can slip in my back pocket or put in a slipper case of some kind on my belt. I need to run by BestBuy and see what they have in the way of cases.