Well, the first one I got (it arrived before the phone did!) was http://www.amazon.co.uk/Samsung-Gala.../dp/B007NL5EC8 - cheap and cheerful and it seems to provide a surprising amount of protection.
Although the one it's in at the moment is one of these http://www.proporta.com/product/sams...uminium-lining. Interesting thing about that one (other than the fact that it's a bit on the expensive side) is that it comes in either "flip up" or "flip down" version. I went for the "flip down" version on the basis that the design means that the front flap stays out of the way (due to gravity) when you're making a call.
Good thing about the S3 (as remarked to me by folks who've got other phones with a touch of envy when they say it) is that it's seen as a "fashion" phone like the iPhone, so there's a lot of "designer" cases out there - NafNaf, Quicksilver, Oakley, Burberry, etc. Nice to be spoilt for choice!
Screen protectors were an essential for me too (because I'm a klutz) and the best ones I've found so far have been the disGuard ones - come in mirror, "crystal" and anti-reflective. I've got the matt finish (anti-reflective) on at the moment and it's very good. Only drawback of the disGuard films is that they're cut too small, so there's two very small triangular areas of screen left uncovered and fitting has to be exact, (lack of spare width). Downside #2 is the mirror ones - they're VERY reflective, although also very thick and laughably easy to apply (apart from the aforementioned smallness).
Slightly off topic, but I really like the S3 - the only drawbacks I've found are an inability to replace the dial tones with something other than "plop plop" and the GPS seems to get very easily confused. Apart from that it's been pretty good.