How to Root/Update OS for a Straight Talk branded Galaxy S3?

[AC Question]

I've had my Galaxy S3 for a little over a year and I would like to update the software to something more current than the stock OS that came with the phone. (4.1.2) The phone, and the carrier that I currently am with, is Straight Talk...but they are notorious for not allowing users to update the software on their Android phones. Is it possible for me to root my phone so I can update the software? I know the S3 is capable of having an operating system that isn't as dated as mine.