Kyle, this is for you, and anyone else who might have a Verizon Galaxy S3 phone. I just rooted and rom'd mine and so far so good. Running the Synergy rom for now.
This link is how to root. There's a video walk through that helps a lot and makes it almost impossible to screw up. Just a few files to download and take less than 10 minutes. You have two options for custom recoveries (Step 5), CWM and TWRP, the TWRP is supposed to be much better and is what I'm using.
http://forum.xda-developers.com/show....php?t=2046439
And here's the Rom that I'm currently running. I've only been rooted for about 10 minutes but I like it so far.
http://forum.xda-developers.com/show....php?t=1792499