Find a training counselor...
First thing you need to do is find an NRA training counselor. If you want to teach the UT class, you must take a UT BCI class in addition to being an NRA certified instructor. UT BCI changed that requirement last summer. You must travel to Utah for that. Since I go up there anyway, it's no big deal for me to recert with UT BCI every three years. Quite a few out of State UT instructors are not renewing because of that requirement.
Usually the lowest grade of NRA instructor you must obtain to become a CCW instructor is NRA Personal Protection inside the Home.
Florida just requires you to be a certified instructor. If all you want to do is teach a Florida accepted CCW class being an NRA certified instructor will work.
Several States also require that not only you be an NRA certified instructor, but you also must conduct classes for their respective CCW within the State of issuance and be registered as an instructor with the AG, County Sheriff or State Police/DPS. Some of them such as AZ have a special instructor class you must take in addition to being registered with them as instructor.