Welcome to Android Forums!
I've not used those other programs, so I cannot answer that directly. Odin is used to flash the phone when it's in download mode. You have to use Odin if, for example, your recovery isn't working. I would think this is how providers flash phones.
There is a rooted VRALG7 and procedure out there:
Download Verizon Galaxy S3 VRALG7 OTA Update, already rooted and deodexed!
I have not tested this, so I cannot author validated step-by-step procedures for it. The target of my guide is anyone who wants to root but hasn't done any of this before or who's intimidated by the process; VRALG7 adds more complexity (by requiring an unlocked boot-loader) with little-to-no upside (and I don't want VZW's snooping software). Anyone else comfortable or familiar with rooting can still use the guide but can also combine it with other resources.
I'll include the aforementioned link in the OP though.