I don't have a GS3 but I love to use different launchers and keyboards with my Razr Maxx. I also like the live sports wallpapers too. I might not be in high school or college anymore but I still like to have fun with my phone some.
I rooted mine a long time ago, I am on Sprint. Rooting allows me to freeze or remove system apps and when I make the 2 hour trip to my Dad's house my daughter can tether her Nexus 7 without the $20 tether charge. I also have some apps that you have to be rooted to use, like Root Call Blocker, that blocks calls at the system level, they don't connect ao the phone never rings.
I have an unlock code from T-Mobile for my Galaxy S3, but the procedure requires me to insert a SIM card from another carrier like AT&T. I can't seem to find someone that I know well enough to ask to borrow their SIM card for a minute.