This is a tough question, D! You almost have to have been diving for a while to know why certain questions are important & others irrelevant. It is not just the instructor but the program. How close are you to the dive sites you will be visiting anyway? If you are going to have t drive to a coastal town to do the dives anyway, perhaps the bigger city is a good choice.
How long is the program? Are they snowing you with the notion that you don't need classroom instruction if you get the video & watch it ahead of time? (The videos ARE good, but a new person is going to have questions that deviate form the pre-fab format.) Do you get a number of dives in different local conditions or is this just a set-up to sell you trips chartered thru the shop? (If you are rich, this does not matter, but to be a GOOD diver, you need to dive as much as possible, even if this means in quarries.)
I have not dived in Tenn., so I do not know what this gorgeous state offers to underwater types, but you may want to look up some sites in your locale & find out what type of diving you will need to learn to stay wet between trips to the Caymans. IE: do you need to know altitude diving because all of the good local sites are in mountain lakes? Do you need to know how to manage yourself in a thick-ish wetsuit (presents the need to develope good buoyancy skills over time.) Is shore diving an option (will save you TONS of money in the long run) or are boats the only way to access your local sites?
I took a long course (multiple months) when I began, but I have friends who took short courses (a weekend!) I would have washed out if I tried to "sink or swim" in a tight amount of time. Also, some very short courses may sound like a bargain, but the idea is to sell you more classes (as you will not have the confidence level to be independent from your instructor after the first 1, 2, or 3 classes.) If the saleman (instructor) has a cavalier attitude about the amount of time it takes to go from being a student to a diver, he may be more into the sale than your safety.
I have a great time with this sport & support anyone who wants to get wet, but I won't lie about the learning curve; some people catch on very quickly due to previous watersport experience, but it is impossible to know which of your own primal fears may emerge in the process of learning. NObody can rush you to stop being scared; you just need time with a very calm person. Look for eye contact - expereinced instructors are practically mimes underwater. Sense sensitivity to the emotional needs of others. I would not send my worst enemy to a "macho" guy because the dynamic of daredevil-ness in inappropriate situations is contagious. Ego is universal in instructors. They really HAVE saved lives, so don't be too put off if they brag a bit. HOwever, this is about YOU; if they talk of past students only in a trophy sense, they are not connecting well with humans & only thinking of their own standing in the diving community.
Sorry so verbose. I wish there was an easy zen-like answer. Too bad you don't live in Florida; I'd say "call Walter."