General :: Root GS3 And Install CyanogenMod 10.1

My current GS3 apparently had water damage, and a new one is coming from the insurance tomorrow. I figured that since the warranty is up and the insurance won't replace it again, I may as well finally root and flash a custom rom. From my poking around the internet, I like CyanogenMod 10.1. I am on AT&T.

I've only attempted a root once before with this current phone, which I think worked, but I abandoned the project months ago and don't remember. In any case, besides that, I've never rooted or flashed a rom before.

After further poking around on the internet, these are the sources I'm planning on using to successfully root and rom:

Rooting: How to Root the Samsung Galaxy S3 " XDA Developer TV " xda-developers

And for the ROM, I'm going to follow this video:

I understand that after rooting, I have to create a backup (using that Titan Backup app in the video I think?" and i am going to use Goo Manager to download the ROM and gapps. I saw another video that had me move files from the computer to my phone, but they didn't do any backing up, and apparently that's necessary.

What does it mean to "trip a flash counter"? And what is a toolkit, and do I need it?