I've rooted many phones, maybe this is good advice -
1. Read, read and read some more before rooting. Our forums contain rooting guides to help with that.
2. Don't panic. Usually, it's going to go smoother than you thought, but every so often, you can stuck. It's happened to me. If that happens, don't panic, and don't try to fix it. Just post what happened and so forth and someone who's been there will guide you along.
3. ONLY root with methods and software known to work for your device. The S3 is a generic model, but slight differences due to carrier variations can require changes in rooting. That's why MP wants to know your carrier. Rooting is not a generic deal.
Once we know that, we'll move this thread over to the right root forum with fellow SGS3 owners with your specific version can give you the exact guidance you need.
Hope this helps!