Hey there. I just created an account since I got my SGS3 recently. This will be my cherry popping post.
I picked up a case off Amazon called Rearth Ringke. It's like a slim snap-on case with a matte finish. I bought both the white and black cases to try out. I ended up using the black case, the one with matte finish, because the white one felt a bit too slippery. I really like the way the case feels and looks. It's ultra slim, but provides a really sleek look and it fits like perfectly. I've actually dropped my phone, in this short amount of time, more times than I'd like to admit. The case has a few blemishes, but my phone is completely intact - although that just might be the phone being a brick as well.
I also tried a few different screen protectors out. My first screen protector was a random brand I picked up off Amazon as well. It was the three-pack price effective protectors. I didn't really like the feel very much, but it did its job. I ended doing a bit more research and a friend recommended checking out the brand Armorsuit. The protector isn't cheap (price-wise), but it's definitely a fair price - just a little bit cheaper than Zagg (my original option). It's actually a wet application, so I was a bit confused at first. I ended up watching some of their instructional videos and the installation was cake. It's been a few weeks and this protector still looks pretty good. Any time I "scratch" it, the marks go away after awhile. I'm actually pretty happy with this.
Let me know which cases and protectors you guys use. I'm down to try a few different brands if they sound worth it.