Default Note III adn TMO

Hey all,
I am a TMO user. I currently have a Galaxy SIII, however I am ready to upgrade to the NOTE III because I need a bigger screen. getting old. Questions:

1. What is the correct model number I need to use with TMO?
2. Where is the best place to purchase one that is rooted and unlocked (factory hopefully)
3. Any other suggestions on a bigger screen phone will be greatly appreciated.

Thanks in Advance