If you're going to start messing around with ROMs and serious modding, you'll need a custom recovery. There are a few popular ones, but TWRP is the go-to for most devices. Getting official support on your device of choice is cause for celebration, and today Note 3 owners on Verizon get to party.
The official build of TWRP for the Verizon Note 3 can be downloaded from the TeamWin website. It's based on the 2.8 branch that just came out recently. You'll have to get the version of the file that matches the installation method you plan to use—there's the regular flashable ZIP, ADB DD image, and the Odin flashable image.
As usual, proceed with caution. Verizon won't be very understanding if you break your device flashing custom recoveries.