You don't need to root to get a stock jellybean release on your phone. You would use a program called odin and put your phone into download mode and it will flash the system on your phone. If you don't like it or need to warranty your phone you just odin back to a official verizon release.
You can follow this guide, you would need 1,2,and 8. Then just follow the steps included.
http://xdaforums.com/showthread.php?t=1974114
Rooting is something you would do if you wanted to run apps or alter system files that require special privileges to access, read or write. A good reason to root is flash a custom recovery. The custom recovery will allow you to make backups of your phone. If something breaks on your system you can simply restore a backup in like 10 mins and its good as new
If you want to flash a rom then you will need to rooted AND have your bootloader unlocked. Its a pretty easy process to do everything as long as you pay attention. I.e. don't flash a rom meant for another carriers S3 or the international S3 cause you will hard brick your phone and have to mail it to someone with like $60 to get it fixed
A good rom to try first would be CleanRom imo. There are many guides around this forum, just read em and reread em then go at it. If you are unsure about something then ask before you do it.
P.s. Backup your imei...... here is a great guide on how to do everything...
http://xdaforums.com/showthread.php?t=1762709